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How to Introduce Group Members in a Presentation Script

How to Introduce Group Members in a Presentation Script

In a presentation script, introduce group members by briefly stating their names and roles. In this introduction, we will discuss the best ways to introduce group members in a presentation script, ensuring clarity and engagement with the audience.

A well-crafted introduction can set the tone for a successful presentation. When introducing group members, it is essential to provide concise information about their names and roles, allowing the audience to understand the expertise each member brings to the table.

By effectively introducing group members, you create a connection between the audience and the presenters, fostering trust and interest in the presentation content. We will explore various strategies and tips for introducing group members in a presentation script while adhering to SEO-friendly writing principles. Let’s dive in and discover how to make impactful introductions for group members in your next presentation script.

Table of Contents

The Importance Of Introducing Group Members In A Presentation Script

Introducing group members in a presentation script holds great importance. It helps establish credibility and build trust. By introducing the team, you create a personal connection with the audience. This allows them to understand the expertise and diversity within the group.

Moreover, it gives each team member a chance to showcase their strengths and contributions. By highlighting individual roles, the audience gains a comprehensive understanding of the presentation’s content. Furthermore, introducing group members fosters a collaborative and professional environment. It shows that the team is well-prepared and unified in their goals.

Overall, introducing group members in a presentation is essential for effective communication and successful outcomes.

Elements Of A Successful Group Member Introduction

Elements of a Successful Group Member Introduction include creating a powerful opening statement, providing background information, and highlighting key skills. Starting with a captivating statement grabs the audience’s attention. Sharing relevant background information about each team member builds credibility. Highlighting key skills and expertise establishes their qualifications.

A concise and engaging introduction sets the tone for the presentation, making it more memorable and impactful. By following these guidelines, you can ensure that your group member introductions are effective and leave a lasting impression on your audience. So, be strategic in your approach and craft introductions that truly showcase the talent and capabilities of your team members.

Crafting An Engaging Presentation Script

Crafting an engaging presentation script involves setting the tone and capturing the audience’s attention from the start. To achieve this, structuring the script for smooth transitions is essential. Rather than simply listing the group members, incorporate storytelling techniques to make the introductions memorable.

By crafting a narrative around each member, you create a connection with the audience, allowing them to relate and engage with the individuals. Use anecdotes, interesting facts, or unique qualities to highlight each person’s contribution. This not only adds a personal touch but also keeps the audience engaged throughout the presentation.

Remember, an effective presentation script is not just about delivering information but also creating a compelling and memorable experience for the listeners. So, take the opportunity to make your introductions stand out and leave a lasting impression on your audience.

Begin With A Captivating Hook

Begin your presentation script with a captivating hook to engage your audience. Capture their attention with a powerful quote or statistic, highlighting the importance of group members in presentations. Share an intriguing anecdote that relates to the topic, sparking curiosity and stimulating their interest.

To provoke thoughtful reflection, ask a question that encourages the audience to consider the significance of working as a team in a presentation setting. By starting strong, you create a compelling opening that sets the tone for an impactful and engaging presentation.

Introducing Each Group Member

Introducing each group member is essential for establishing credibility and expertise. By sharing relevant accomplishments and experiences, you highlight their value to the team. Highlighting their areas of expertise can boost their credibility and gain the audience’s trust. Use concise sentences to mention their key achievements and qualifications.

It is crucial to showcase how each member’s unique skills contribute to the team’s success. By doing so, you ensure that the presentation is informative and engaging. Introducing each group member allows the audience to connect with them on a personal level, making the presentation more relatable and memorable.

Ultimately, effective introductions help establish a strong foundation for a successful presentation.

How to Introduce Group Members in a Presentation Script

Credit: fellow.app

Connecting Group Members To The Presentation Topic

Introducing group members in a presentation script involves connecting them to the topic at hand. By demonstrating how each team member’s expertise aligns with the subject matter, the audience gains insight into their contributions. Additionally, showcasing the unique perspectives of each member enhances the overall presentation, enriching it with diverse viewpoints.

Moreover, emphasizing the collective knowledge and capabilities of the team highlights their collaborative efforts. This approach creates a cohesive and well-rounded presentation, capturing the audience’s attention. It is important to avoid generic and overused phrases while introducing group members in order to maintain the reader’s interest.

By following these guidelines, you can effectively introduce group members in your presentation script while keeping your audience engaged and informed.

Tips For A Fluent And Natural Delivery

Introducing group members in a presentation script can greatly enhance the effectiveness of your delivery. To ensure a fluent and natural delivery, it is important to practice the script beforehand. By using conversational language and tone, you can engage the audience and make them feel more connected to your presentation.

Eye contact and body language also play a crucial role in keeping the audience engaged and interested. Make sure to maintain eye contact with individuals throughout your presentation and use gestures and movements to emphasize key points. This will create a positive and interactive atmosphere, increasing the impact of your presentation.

So remember, practice your script, use conversational language, and engage your audience through eye contact and body language for a successful presentation.

Avoiding Common Mistakes In Group Member Introductions

Group member introductions in a presentation script should be concise and balanced, ensuring that no member is neglected. When introducing each member, avoid using jargon or technical terms that may confuse the audience. It is important not to overwhelm the listeners with excessive information.

Keep it simple and straightforward, providing only relevant details about each member’s role and expertise. By doing so, you can engage the audience and maintain their interest throughout the presentation. Clear and concise introductions create a positive impression and help establish credibility among the group members.

So, remember to be mindful of these common mistakes and deliver effective introductions that leave a lasting impact on your audience.

Frequently Asked Questions On How To Introduce Group Members In A Presentation Script

How do you start a group presentation introduction script.

To start a group presentation introduction, follow these simple steps. Begin with a catchy opening line to grab the audience’s attention. Introduce yourself and your group members briefly, sharing relevant qualifications or expertise. Next, outline the purpose of your presentation and how it will benefit the audience.

Transition into providing an overview of the main topics you will cover, using succinct and engaging language. Lastly, conclude the introduction by highlighting the key takeaways or outcomes your audience can expect. Remember to speak confidently and maintain eye contact with the audience to enhance your delivery.

By following these steps, you can set a strong foundation for a successful group presentation.

How To Introduce Myself And My Group Members In A Presentation Script?

In a presentation script, introducing yourself and your group members can be done in a concise and engaging manner. Begin by stating your name and role within the group. Then, briefly mention the expertise or qualifications that make you suitable for the presentation.

Transition smoothly to introducing each group member by mentioning their names and roles, along with a key attribute or achievement. This will highlight their credibility and relevance to the topic. Remember to focus on the value they bring to the presentation.

By keeping your introductions short and informative, the audience will quickly grasp who you are and why you are qualified to speak on the topic. This establishes credibility and sets the stage for an impactful presentation.

How Do You Introduce Team Members In A Script?

To introduce team members in a script, use concise sentences to keep the information clear and engaging. Start by stating each team member’s name and their role or position within the team. For example, “John Smith is our creative director,” or “Sarah Jones is our marketing specialist.

” Highlight each team member’s expertise and relevant experience, showcasing their unique contributions to the team’s success. Use positive and descriptive language to make their introductions more captivating. Consider adding a personal touch by mentioning their hobbies or interests related to their work.

This will help create a connection between the team members and the audience. Remember to keep the introductions brief to maintain the script’s flow and overall impact.

How Do You Introduce A Team Member In Powerpoint?

To introduce a team member in PowerPoint, follow these simple steps. First, open PowerPoint and navigate to the slide where you want to introduce the team member. Then, click on the “Insert” tab in the top menu and select “Text Box” from the options.

In the text box, type the name and position of the team member. Next, click on the “Design” tab and choose a suitable layout or design for the slide. You can also add a photo of the team member by clicking on the “Insert” tab again and selecting “Picture”.

Once you have entered the necessary information and customized the slide, you can present it by clicking on the “Slide Show” tab and selecting “From Beginning”. This will allow you to introduce your team member to your audience effectively and visually.

Introducing group members in a presentation script is a crucial aspect of delivering a successful presentation. By following a structured approach, you can effectively introduce your team members, create a positive impression, and engage your audience. Start by explaining the purpose and relevance of introducing the group members to establish their credibility.

Be sure to provide essential details like names, roles, and expertise, highlighting their qualifications and achievements. Utilize storytelling techniques and incorporate personal anecdotes to make the introductions more relatable and captivating. Remember to maintain a consistent flow and pace throughout the script, ensuring that each team member’s introduction seamlessly transitions into the next.

By following these guidelines, you can effectively introduce group members in your presentation script, creating a dynamic and engaging experience for your audience.

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Blog Marketing How To Start a Presentation: 15 Ways to Set the Stage

How To Start a Presentation: 15 Ways to Set the Stage

Written by: Krystle Wong Jul 25, 2023

How To Start A Presentation

The opening moments of your presentation hold immense power – it’s your opportunity to make a lasting impression and captivate your audience. 

A strong presentation start acts as a beacon, cutting through the noise and instantly capturing the attention of your listeners. With so much content vying for their focus, a captivating opening ensures that your message stands out and resonates with your audience.

Whether you’re a startup business owner pitching a brilliant idea, a seasoned presenter delivering a persuasive talk or an expert sharing your experience, the start of your presentation can make all the difference. But don’t fret — I’ve got you covered with 15 electrifying ways to kickstart your presentation. 

The presentation introduction examples in this article cover everything from self-introduction to how to start a group presentation, building anticipation that leaves the audience eager to delve into the depths of your topic.

Click to jump ahead:

How to start a presentation introduction

15 ways to start a presentation and captivate your audience, common mistakes to avoid in the opening of a presentation, faqs on how to start a presentation, captivate the audience from the get-go.

introducing group in presentation

Presentations can be scary, I know. But even if stage fright hits, you can always fall back on a simple strategy.

Just take a deep breath, introduce yourself and briefly explain the topic of your presentation.

To grab attention at the start, try this opening line: Hello everyone. I am so glad you could join me today. I’m very excited about today’s topic. I’m [Your Name] and I’ll be talking about [Presentation Topic]. Raise your hand if you’ve ever felt overwhelmed by [Challenge related to your topic]. Many of us might have faced challenges with [Challenge related to your topic]. Today, we’ll explore some strategies that’ll help us [Solution that you’re presenting].

Regardless of your mode of presentation , crafting an engaging introduction sets the stage for a memorable presentation.

Let’s dive into some key tips for how to start a presentation speech to help you nail the art of starting with a bang:

Understand your audience

The key to an engaging introduction is to know your audience inside out and give your audience what they want. Tailor your opening to resonate with their specific interests, needs and expectations. Consider what will captivate them and how you can make your presentation relevant to their lives or work.

Use a compelling hook

Grab the audience’s attention from the get-go with a compelling hook. Whether it’s a thought-provoking question, a surprising fact or a gripping story, a powerful opening will immediately pique their curiosity and keep them invested in what you have to say.

introducing group in presentation

State your purpose

Be crystal clear about your subject matter and the purpose of your presentation. In just a few sentences, communicate the main objectives and the value your audience will gain from listening to you. Let them know upfront what to expect and they’ll be more likely to stay engaged throughout.

Introduce yourself and your team

Give a self introduction about who you are such as your job title to establish credibility and rapport with the audience.

Some creative ways to introduce yourself in a presentation would be by sharing a brief and engaging personal story that connects to your topic or the theme of your presentation. This approach instantly makes you relatable and captures the audience’s attention.

Now, let’s talk about — how to introduce team members in a presentation. Before introducing each team member, briefly explain their role or contribution to the project or presentation. This gives the audience an understanding of their relevance and expertise.

Group presentations are also a breeze with the help of Venngage. Our in-editor collaboration tools allow you to edit presentations side by side in real-time. That way, you can seamlessly hare your design with the team for input and make sure everyone is on track. 

Maintain enthusiasm

Enthusiasm is contagious! Keep the energy levels up throughout your introduction, conveying a positive and upbeat tone. A vibrant and welcoming atmosphere sets the stage for an exciting presentation and keeps the audience eager to hear more.

Before you think about how to present a topic, think about how to design impactful slides that can leave a lasting impression on the audience. Here are 120+ presentation ideas , design tips, and examples to help you create an awesome slide deck for your next presentation.

Captivating your audience from the get-go is the key to a successful presentation. Whether you’re a seasoned speaker or a novice taking the stage for the first time, the opening of your presentation sets the tone for the entire talk. 

So, let’s get ready to dive into the 15 most creative ways to start a presentation. I promise you these presentation introduction ideas will captivate your audience, leaving them hanging on your every word.

Grab-attention immediately

Ask a thought-provoking question.

Get the audience’s wheels turning by throwing them a thought-provoking question right out of the gate. Make them ponder, wonder and engage their critical thinking muscles from the very start.

Share a surprising statistic or fact

Brace yourself for some wide eyes and dropped jaws! Open your presentation with a jaw-dropping statistic or a mind-blowing fact that’s directly related to your topic. Nothing captures attention like a good ol’ dose of shock and awe.

introducing group in presentation

State a bold statement or challenge

Ready to shake things up? Kick off with a bold and daring statement that sets the stage for your presentation’s epic journey. Boldness has a way of making ears perk up and eyes widen in anticipation!

Engage with a poll or interactive activity

Turn the audience from passive listeners to active participants by kicking off with a fun poll or interactive activity. Get them on their feet, or rather — their fingertips, right from the start!

Venngage’s user-friendly drag-and-drop editor allows you to easily transform your slides into an interactive presentation . Create clickable buttons or navigation elements within your presentation to guide your audience to different sections or external resources. 

Enhance engagement by incorporating videos or audio clips directly into your presentation. Venngage supports video and audio embedding, which can add depth to your content.

introducing group in presentation

Begin with an opening phrase that captures attention

Use opening phrases that can help you create a strong connection with your audience and make them eager to hear more about what you have to say. Remember to be confident, enthusiastic and authentic in your delivery to maximize the impact of your presentation.

Here are some effective presentation starting words and phrases that can help you grab your audience’s attention and set the stage for a captivating presentation:

  • “Imagine…”
  • “Picture this…”
  • “Did you know that…”
  • “Have you ever wondered…”
  • “In this presentation, we’ll explore…”
  • “Let’s dive right in and discover…”
  • “I’m excited to share with you…”
  • “I have a confession to make…”
  • “I want to start by telling you a story…”
  • “Before we begin, let’s consider…”
  • “Have you ever faced the challenge of…”
  • “We all know that…”
  • “This is a topic close to my heart because…”
  • “Over the next [minutes/hours], we’ll cover…”
  • “I invite you to journey with me through…”

Build connection and credibility

Begin with a personal connection .

Share a real-life experience or a special connection to the topic at hand. This simple act of opening up creates an instant bond with the audience, turning them into your biggest cheerleaders.

Having the team share their personal experiences is also a good group presentation introduction approach. Team members can share their own stories that are related to the topic to create an emotional connection with your audience. 

introducing group in presentation

Tell a relevant story

Start your presentation with a riveting story that hooks your audience and relates to your main message. Stories have a magical way of captivating hearts and minds. Organize your slides in a clear and sequential manner and use visuals that complement your narrative and evoke emotions to engage the audience.

With Venngage, you have access to a vast library of high-quality and captivating stock photography, offering thousands of options to enrich your presentations. The best part? It’s entirely free! Elevate your visual storytelling with stunning images that complement your content, captivate your audience and add a professional touch to your presentation. 

Venngage Stock Photo Library

Use a powerful quote

Sometimes, all you need is some wise words to work wonders. Begin with a powerful quote from a legendary figure that perfectly fits your presentation’s theme — a dose of inspiration sets the stage for an epic journey.

Build anticipation

Provide a brief outline.

Here’s a good introduction for presentation example if you’re giving a speech at a conference. For longer presentations or conferences with multiple speakers especially, providing an outline helps the audience stay focused on the key takeaways. That way, you can better manage your time and ensure that you cover all the key points without rushing or running out of time.

Pose a problem and offer a solution

A great idea on how to start a business presentation is to start by presenting a problem and offering a well-thought-out solution. By addressing their pain points and showcasing your solution, you’ll capture their interest and set the stage for a compelling and successful presentation.

Back up your solution with data, research, or case studies that demonstrate its effectiveness. This can also be a good reporting introduction example that adds credibility to your proposal.

Preparing a pitch deck can be a daunting task but fret not. This guide on the 30+ best pitch deck tips and examples has everything you need to bring on new business partners and win new client contracts. Alternatively, you can also get started by customizing one of our professional pitch deck templates for free. 

introducing group in presentation

Incite curiosity in the audience

Utilize visuals or props.

Capture your audience’s gaze by whipping out captivating visuals or props that add an exciting touch to your subject. A well-placed prop or a stunning visual can make your presentation pop like a fireworks show!

That said, you maybe wondering — how can I make my presentation more attractive.  A well-designed presentation background instantly captures the audience’s attention and creates a positive first impression. Here are 15 presentation background examples to keep the audience awake to help you get inspired. 

Use humor or wit

Sprinkle some humor and wit to spice things up. Cracking a clever joke or throwing in a witty remark can break the ice and create a positively charged atmosphere. If you’re cracking your head on how to start a group presentation, humor is a great way to start a presentation speech. 

Get your team members involved in the fun to create a collaborative and enjoyable experience for everyone. Laughter is the perfect way to break the ice and set a positive tone for your presentation!

introducing group in presentation

Invoke emotion

Get those heartstrings tugging! Start with a heartfelt story or example that stirs up emotions and connects with your audience on a personal level. Emotion is the secret sauce to a memorable presentation.

Aside from getting creative with your introduction, a well-crafted and creative presentation can boost your confidence as a presenter. Browse our catalog of creative presentation templates and get started right away!

Use a dramatic pause

A great group presentation example is to start with a powerful moment of silence, like a magician about to reveal their greatest trick. After introducing your team, allow a brief moment of silence. Hold the pause for a few seconds, making it feel deliberate and purposeful. This builds anticipation and curiosity among the audience.

Pique their interest

Share a fun fact or anecdote.

Time for a little fun and games! Kick-off with a lighthearted or fascinating fact that’ll make the audience go, “Wow, really? Tell me more!” A sprinkle of amusement sets the stage for an entertaining ride.

While an introduction for a presentation sets the tone for your speech, a good slide complements your spoken words, helping the audience better understand and remember your message. Check out these 12 best presentation software for 2023 that can aid your next presentation. 

introducing group in presentation

The opening moments of a presentation can make or break your entire talk. It’s your chance to grab your audience’s attention, set the tone, and lay the foundation for a successful presentation. However, there are some common pitfalls that speakers often fall into when starting their presentations. 

Starting with Apologies

It might be tempting to start with a preemptive apology, especially if you’re feeling nervous or unsure about your presentation. However, beginning with unnecessary apologies or self-deprecating remarks sets a negative tone right from the start. Instead of exuding confidence and credibility, you’re unintentionally undermining yourself and your message. 

Reading from Slides

One of the most common blunders in the opening of a PowerPoint presentation is reading directly from your slides or script. While it’s crucial to have a well-structured outline, reciting word-for-word can lead to disengagement and boredom among your audience. Maintain eye contact and connect with your listeners as you speak. Your slides should complement your words, not replace them.

introducing group in presentation

Overwhelming with Information

In the excitement to impress, some presenters bombard their audience with too much information right at the beginning.

Instead of overloading the audience with a sea of data, statistics or technical details that can quickly lead to confusion and disinterest, visualize your data with the help of Venngage. Choose an infographic template that best suits the type of data you want to visualize. Venngage offers a variety of pre-designed templates for charts, graphs, infographics and more.

Venngage Infographics Templates

Ignoring the Audience

It’s easy to get caught up in the content and forget about the people in front of you. Don’t overlook the importance of acknowledging the audience and building a connection with them. Greet them warmly, make eye contact and maintain body language to show genuine interest in their presence. Engage the audience early on by asking a show of hands question or encourage audience participation. 

Lack of Clarity

Your audience should know exactly what to expect from your presentation. Starting with a vague or unclear opening leaves them guessing about the purpose and direction of your talk. Clearly communicate the topic and objectives of your presentation right from the beginning. This sets the stage for a focused and coherent message that resonates with your audience.

Simplicity makes it easier for the audience to understand and retain the information presented. Check out our gallery of simple presentation templates to keep your opening concise and relevant. 

introducing group in presentation

Skipping the Hook

The opening of your presentation is the perfect opportunity to hook your audience’s attention and keep them engaged. However, some presenters overlook this crucial aspect and dive straight into the content without any intrigue. Craft an attention-grabbing hook that sparks curiosity, poses a thought-provoking question or shares an interesting fact. A compelling opening is like the key that unlocks your audience’s receptivity to the rest of your presentation.

Now that you’ve got the gist of how to introduce a presentation, further brush up your speech with these tips on how to make a persuasive presentation and how to improve your presentation skills to create an engaging presentation . 

introducing group in presentation

How can I overcome nervousness at the beginning of a presentation?

To overcome nervousness at the beginning of a presentation, take deep breaths, practice beforehand, and focus on connecting with your audience rather than worrying about yourself.

How long should the opening of a presentation be?

The opening of a presentation should typically be brief, lasting around 1 to 3 minutes, to grab the audience’s attention and set the tone for the rest of the talk.

Should I memorize my presentation’s opening lines?

While it’s helpful to know your opening lines, it’s better to understand the key points and flow naturally to maintain authenticity and flexibility during the presentation.

Should I use slides during the opening of my presentation?

Using slides sparingly during the opening can enhance the message, but avoid overwhelming the audience with too much information early on.

How do I transition smoothly from the opening to the main content of my presentation?

Transition smoothly from the opening to the main content by providing a clear and concise outline of what’s to come, signaling the shift and maintaining a logical flow between topics.

Just as a captivating opening draws your audience in, creating a well-crafted presentation closing has the power to leave a lasting impression. Wrap up in style with these 10 ways to end a presentation .

Presenting virtually? Check out these tips on how to ace your next online presentation . 

Captivating your audience from the very beginning is crucial for a successful presentation. The first few moments of your talk can set the tone and determine whether your audience remains engaged throughout or loses interest. 

Start with a compelling opening that grabs their attention. You can use a thought-provoking question, a surprising statistic or a powerful quote to pique their curiosity. Alternatively, storytelling can be a potent tool to draw them into your narrative. It’s essential to establish a personal connection early on, whether by sharing a relatable experience or expressing empathy towards their needs and interests.

Lastly, be mindful of your body language and vocal delivery. A confident and engaging speaker can captivate an audience, so make eye contact, use appropriate gestures and vary your tone to convey passion and sincerity.

In conclusion, captivating your audience from the very beginning requires thoughtful preparation, engaging content and a confident delivery. With Venngage’s customizable templates, you can adapt your presentation to suit the preferences and interests of your specific audience, ensuring maximum engagement. Go on and get started today!

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PresentationLoad

Introducing Your Team in Company Presentations: 4 Great Ideas!

You’ve probably already had to introduce your team within a company presentation: in 2023, this is no longer a rarity. Presentations which require you to talk about your company structure, or onboardings, for example, are going to need a team introduction, and knowing how to clearly visualize your team is a useful skill.

Why introduce your team in a presentation?

Introducing your team is a great way to positively influence public perception and to present the strengths and achievements of your company .

Products are rarely developed by individuals working on their own, so companies should never miss an opportunity to showcase the teams responsible for tomorrow’s innovations. This tends to increase stakeholder confidence and generate interest.

Involving your team in your presentations is essential to highlighting both the competence of your employees and your skills as a leader . At the same time, you double down on the authenticity of your presentation and acknowledge your colleagues’ performance, which in turn boosts their self-esteem. The positive impact of even a single slide in a presentation should not be underestimated!

Team introductions are brilliant for onboarding , where you can clearly and transparently visualize your company hierarchy.

Why not browse the PowerPoint templates for onboarding that we at PresentationLoad have put together for you?

Onboarding slides to introduce your team

Bonus tip: Paste images faster with the Scan&Paste app

Pictures generate feelings. This applies to team introductions as well as more generally. If people can see what a particular employee looks like, they’re more likely to want to build connections than if they’re just described in words.

To help you quickly and easily insert images of your team into your presentations, a great tip is to use the Scan&Paste app . This app allows you to upload images directly from your smartphone gallery through a PowerPoint add-in. We’ve covered this for you in our blog post “ Scan&Paste-App “.

4 great ideas to optimize your PowerPoint team presentation!

You want the team introduction in your company presentation to be memorable, right? Here are four great ideas to achieve just that!

  • Use an organizational chart

One way to visualize your team structures is to use an organizational chart, or org chart. Their visual clarity and simplicity make them ideal for showing how teams work.

Org charts show at a glance how a team fits together and how different employees relate to each other. They might not be the most exciting things in the world, but they are really effective . Keep your org chart as simple as possible, though; overloading it will be counterproductive.

Use high-quality pictures of your employees. Your main focus should be on clarity: choose a clear, clean design, make sure people’s names are legible, and avoid unnecessary lines and cross-connections. We’ve covered how to create an org chart quickly and easily yourself in our article “ Creating an organizational chart “.

Why not use PresentationLoad’s organizational charts template to introduce your team?

Organigramm Toolbox Shop 1

  • Rounded Photos

You can also introduce your team in the classic way, using text to cover the most important key points , and adding visual interest in a modern and stylish way by using rounded pictures .

PresentationLoad have got this covered too! You can find them here .

Including a team introduction in your presentation

There are several ways of introducing your team – here are a few of the best:

Idea #1: Team Slide

The simplest way to introduce your team is by means of a team slide . This should show high-quality images of your team, either individually or in a group photo.

Keep text to an absolute minimum here.  Anything more than the names of your employees can be distracting.  You can go into greater detail in your narration.

The advantage of a team slide is that you can clearly show all the important people on one slide.

A team slide might look something like this:

Team Slide to introduce your ten

The disadvantage of such a simple slide is that it shows little in the way of a team structure. If you need to show this, go with idea #2.

Idea #2: Team Structure

A team structure slide obviously shows how your team is structured, meaning it’s clear who works for whom and how responsibilities are divided up.  They are perfect for onboarding, for example, allowing new employees to easily recognize internal structures and contact persons.

Keep in mind that team structures are not necessary for every presentation; team slides can quickly become confusing if there are too many connections. So keep them as clear as possible.

A team structure slide might look something like this:

Content3 EN Team Presentation2

Idea #3: Individual Slides

In some cases it may be useful to introduce your team individually . In this case, you can get all the important information on one slide per person. You’ll need to include a picture and the person’s function within the company as well as their name, and there may also be room for contact details or a short CV . Here’s an example:

Introduce your team with indiviudal slides

Idea #4: Quote slide

A slightly different take on this is the quote slide .  Quotes can be another way to introduce your team’s thinking. Let your employees have their say by including core ideas and statements in your presentation in the form of quotes.

This highlights how important your team is, and emphasizes their individuality and competence. Quotes also help to make your presentation more interesting, which means you get to grab and keep your audience’s attention.

Introduce team with quote slide

Bonus tip: Pay attention to layout in team introductions

When creating your team presentation, don’t forget that your slides need to be visually interesting . Use a clear structure and don’t overcrowd the slides; aim for a good balance of images and text .

We have a lot of useful tips in this respect in our article “PowerPoint Layout”. For example, a picture-text combination slide might come in really handy here. Grids of three or four usefully combine pictures of your team members with just enough text to give the important information:

Introduce your team with special layouts

To sum up: Project your team image effectively in presentations

A team introduction is a great way to introduce your company and its structures within a presentation. Depending on what you need, you can keep it short and introduce your team on one team slide, or go for more detail and use several slides.

Use our tips the next time you need to introduce your business and colleagues, and see how effective they are!

Still have questions about team presentation? Feel free to contact us by email at [email protected] . We’re always happy to help! Interested in great-looking,professionally designed, easy to use slide templates ? Feel free to take a look around our store! We have a huge range of great PPT templates to download, covering just about every business topic you need. Take a look today! ► To the store

You might also be interested in the following articles:

  • 8 tips for company presentations
  • Create an organizational chart with PowerPoint
  • Scan&Paste App: Insert pictures faster
  • PowerPoint layout

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How to Introduce the Next Speaker in a Presentation

Last Updated: March 21, 2024 Fact Checked

This article was co-authored by Patrick Muñoz . Patrick is an internationally recognized Voice & Speech Coach, focusing on public speaking, vocal power, accent and dialects, accent reduction, voiceover, acting and speech therapy. He has worked with clients such as Penelope Cruz, Eva Longoria, and Roselyn Sanchez. He was voted LA's Favorite Voice and Dialect Coach by BACKSTAGE, is the voice and speech coach for Disney and Turner Classic Movies, and is a member of Voice and Speech Trainers Association. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 238,152 times.

Whether at work, school, or a professional conference or workshop, group presentations are something you might find yourself giving from time to time. Introductions are part of any public speaking , so it’s good to know a few guidelines for introducing the person who’s speaking after you in a presentation. We want to help you nail your next presentation , so we put together this list of tips to make transitional introductions a breeze!

Things You Should Know

  • Summarize your main points briefly to wrap up your portion of the presentation.
  • Introduce the next topic to shift the audience's focus into a smooth transition.
  • Praise the upcoming speaker or offer a few details about them. Then, state the speaker's full name and professional title to finish the introduction.

Summarize what you just talked about.

This wraps up your section of the presentation to transition into the next.

  • For example, say something like: “So, in conclusion , if global warming continues at the current rate, more than 140 million people could be displaced by 2050.”
  • Or, say something like: “Well, that was a brief introduction to the projected effects of carbon emissions over the next 3 decades.”

Set the audience up for the next topic with a question.

This gets the audience to shift their focus to the next topic.

  • For example, if the next speaker is going to talk about the implications of AI for future generations, ask something like: “What if by the year 2075 there was no longer any need for humans in manufacturing jobs?”
  • Or, if the next presenter is there to talk about cloud computing security, ask something like: “How often do you worry about security when you save your files to the cloud?”

Say the upcoming speaker’s name.

This lets the audience know exactly who is up next.

  • For example, say: “Up next is Robert Sandoval…”
  • Or, say: “Here now is John Mando…”

State the next presenter’s title or profession.

This tells the...

  • For example, say something like: “Up next is Alex Bando, Marketing Director.”
  • Or, say something like: “Roger Stoney is a former philosophy professor at Washington State University.”

Tell the audience what the next person is there to talk about.

This builds anticipation to get the audience’s attention.

  • For example, after you state the person’s name and background, say something like: “He’s going to talk to you about 5 tried-and-true time management techniques for success that you can start using today!”
  • Or, say something like: “Jill is going to speak about an exciting discovery she made while researching the behaviors of the Puget Sound’s octopus population last year.”

Praise the next speaker as you introduce them.

This shows the audience that you personally endorse the individual.

  • For example, say something like: “Sarah is truly one of the most brilliant minds I’ve met in the world of physics and I can’t wait for you to hear what she has to say.”
  • Or, say something like: “Alexa has been a close colleague of mine for almost 6 years now and she’s a great public speaker, so I know you’re really going to enjoy this.”
  • If you don't know the person personally, you could do a little research about their achievements and say something like: "John has won global recognition for his books and is a leading authority on economics."

Add a fun piece of information or a joke.

A fun fact or a joke can help pique the audience’s attention.

  • For example, say something like: “Besides being a leading expert in marine biology, Jill speaks 5 languages fluently. But don’t worry, this presentation is only in 1!”

Keep the introduction short.

Audiences want to hear what the speaker has to say.

  • For instance, your first sentence is a summary of what you said, your second sentence is a question to frame the upcoming topic, then you can fit the next speaker’s name, title, and topic all into the next 1-2 sentences. Finally, you can end with a fun fact about the next presenter in your fifth sentence.”

Give the next presenter a cue that it’s their time to speak.

This ends the intro and brings the next speaker on stage.

  • You could say something like: “Come on up, Sam!”
  • Or, say: “Welcome, Rachel.”

Rehearse your entire presentation at least twice.

This ensures you get the introduction right.

  • If you can’t rehearse with the speaker you have to introduce, you can still practice your whole section of the presentation up to the end of the transitional intro. Just imagine that the next speaker is sitting off to the side somewhere.
  • It can help to film yourself practicing in front of a mirror and then watching the video back. You can also practice in front of a friend.

Expert Q&A

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Speak on Any Topic

  • ↑ https://www.indeed.com/career-advice/career-development/how-to-conclude-a-presentation
  • ↑ https://hbr.org/2016/10/how-to-memorably-introduce-another-speaker
  • ↑ https://courses.lumenlearning.com/wm-publicspeaking/chapter/introducing-a-speaker/
  • ↑ https://www.meetingsnet.com/speakers-entertainment/4-tips-introducing-your-next-keynote-speaker
  • ↑ https://www.youtube.com/watch?v=f6Xa1fq-oPo&t=120s
  • ↑ https://hbr.org/2019/09/how-to-rehearse-for-an-important-presentation

About This Article

Patrick Muñoz

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Guide for Giving a Group Presentation

February 21, 2018 - Dom Barnard

In certain academic and business situations, it is more valuable to deliver a group presentation than a solo one. Many people prefer group presentations because there is less pressure on the individual. However there are also unique challenges, such as having to ensure multiple individuals collaborate in order to produce a cohesive piece of work.

Preparing for the group presentation

As with any presentation, there is a significant amount of work during the preparation stage. The group must be well organised because there are multiple individuals, and therefore multiple personalities involved.

Presentation moderator

To assist with organisation, the group should first decide on a presentation moderator – this is essentially the “leader”. The presentation moderator can have the final say when decision-making is needed and, during the Q&A portion of the presentation, can decide which speakers will answer certain questions.

Understanding the audience

To make your presentation engaging you need to  think about the audience  so you can tailor it towards their needs. How much will the audience already know about this topic? What will they want to get from this presentation?

For example, if you are presenting the topic of building a bridge to a group of civil engineers, you can confidently use technical language. However, if you are presenting to secondary school students, you would need to use simpler language and not explain the methods in as much detail.

The presentation’s purpose

As a group, ensure you agree on the purpose of the presentation so that you all understand the message that needs to be conveyed e.g. “We want to find out which treatment works best for social anxiety.” Deciding on your message means that the group can start building key points around this – just keep in mind that each subtopic must contribute to the presentation’s aim.

Divide the presentation

The presentation needs to be  divided into main areas  so there is a clear beginning, middle and end. This is where can you decide on the order of the subtopics. Presentations usually follow this structure:

1. Introduction:

  • It is useful to agree on the first minute of the presentation as a team. This is because the audience should be interested from the start and convinced to listen.
  • The presentation’s aims are also discussed and an overview of the presentation’s structure is provided. For example, “We set out to explore the effectiveness of different treatments for social anxiety. We will first cover the symptoms and prevalence of social anxiety, before explaining the different treatments. This will then lead into a discussion about the pros and cons of each treatment route. Finally, we will explain which treatment route we decided was the most effective for this disorder.”

2. One or two middle sections:

  • These sections consist of providing the information that addresses your presentation’s aim.
  • There can be more of these sections depending on your topic.

3. Conclusion:

  • After summarising all of the key points, there must be a clear conclusion. It is beneficial to appoint the conclusion to the best speaker as this is where all the information is pooled together.

After segmenting the presentation, a time sequence can be created so the group understands the order in which tasks must be completed. It is important to set deadlines for this.

Share responsibility

A frequent problem when working within a group is unequal participation as this can subsequently cause disharmony.

But this is easily avoidable by assigning each speaker a section of the presentation to work on depending on their interests. This means that each speaker should be doing the research for their section and putting together a speech and slides (if being used).

  • It is important to specify exactly what each group member should be doing with their time.
  • Make sure the length of time per speaker is agreed on.
  • Do not change speakers more than necessary because this can reduce the coherency of the presentation.

Build the presentation together

For an audience to follow and enjoy a presentation, it must flow together. Meeting up and building the presentation helps with this because:

  • This prevents the duplication of content.
  • You can put the slides together, although only one individual should be responsible for merging the slides so there is consistency within the presentation.
  • It is useful to receive feedback on the speeches before presenting to an audience.
  • The team can agree on any edits.
  • The team can agree on the conclusion.
  • You can make sure that each speaker will talk for the same amount of time and cover a similar amount of information.
  • The team can come up with the first minute of the presentation together.

Business people giving a group presentation

Use stories to engage the audience

A good presentation opening could  start with a story  to highlight why your topic is significant. For example, if the topic is on the benefits of pets on physical and psychological health, you could present a story or a study about an individual whose quality of life significantly improved after being given a dog.

The audience is more likely to remember this story than a list of facts and statistics so try and incorporate relevant stories into presentations.

Know what each speaker will say

Each speaker must know what the other group members will say as this prevents repetition and it may be useful to refer to a previous speaker to assist in explaining your own section.

Also, if a team member is unable to attend on the day it will be easier to find cover within the group.

Write and practice transitions

Clean transitioning between speakers can also assist in producing a presentation that flows well. One way of doing this is:

  • Briefly recap on what you covered in your section: “So that was a brief introduction on what social anxiety is and how it can affect somebody”
  • Introduce the next speaker in the team and explain what they will discuss: “Now Sarah will talk about the prevalence of social anxiety.”
  • Then end by looking at the next speaker, gesturing towards them and saying their name: “Sarah”.
  • The next speaker should acknowledge this with a quick: “Thank you Nick.”

From this example you can see how the different sections of the presentations link which makes it easier for the audience to follow and remain engaged.

Practice the presentation

Rehearse with the group multiple times to make sure:

  • The structure works
  • Everyone is sticking to their timing.
  • To see if any edits are needed.

The more you  rehearse a presentation  the more you will feel comfortable presenting the material and answering questions as your familiarity with the content increases.

Handling nerves before the presentation

It is  natural to feel nervous  when presenting in front of others, regardless of the size of the audience. Here are some tips:

  • Remind yourself that the audience is there to listen to you and wants you to do well; there is no need to be afraid of them.
  • Remember that the audience members will have to present their projects later and are almost certainly feeling just as nervous.
  • Practicing with your group and practicing your section at home will make you more comfortable and familiar with the material and increase your confidence.
  • Practice pauses  – when people feel nervous they tend to find silences uncomfortable and try to fill gaps, such as using “um” multiple times (filler words). Practicing pauses will help the silences feel less unnatural when you present therefore reducing the need for filler words.
  • When we are nervous we often begin breathing quickly and this in turn can increase our anxiety. Controlled breathing is a common technique that helps slow down your breathing to normal thus reducing your anxiety.

Exercises to control your breathing:

  • Sit down in an upright position as it easier for your lungs to fill with air
  • Breathe in through your nose and into your abdomen for four seconds
  • Hold this breathe for two seconds
  • Breathe out through your nose for six seconds
  • Wait a few seconds before inhaling and repeating the cycle

During the group presentation

Introducing the team.

The presentation should begin with the presentation moderator introducing the team. This is smoother than each individual presenting themselves.

Pay attention to the presentation

You may feel nervous as you wait for your turn to speak but try to listen to the presentation. The audience is able to see the whole team so it is important that you look interested in what is being said and react to it, even if you have heard it multiple times.

Body language and eye contact

Body language is a useful tool to engage the audience:

  • If it is your turn to speak then stand slightly in the foreground of the rest of your group.
  • Smile at the audience as this will make you look more confident.
  • Make eye contact  as this helps you engage with the audience.
  • Keep your arms uncrossed so your body language is more open.
  • Do not look down and read from your notes- glancing down occasionally is fine but keep in mind that you are talking to the audience.
  • This is the same for  presenting visual aids ; you may need to glance at the computer slide but make sure you predominantly face the audience as you are still speaking to them.
  • Keep your hands at your sides but use them occasionally to gesture.

Vocal variety

How you say something is just as is important as the content of your speech –  arguably, more so . For example, if an individual presented on a topic very enthusiastically the audience would probably enjoy this compared to someone who covered more points but mumbled into their notes.

Here are some pointers:

  • Adapt your voice depending on what are you saying- if you want to highlight something then raise your voice or lower your voice for intensity.
  • Avoid speaking in monotone.
  • Sound enthusiastic – the more you sound like you care about the topic, the more the audience will listen.
  • Speak loudly and clearly.
  • If you notice that you are speaking quickly, pause and slow down.
  • Warm up your voice  before a speech

Breath deeply for vocal variety

Take short pauses and breath deeply. This will ensure you have more vocal variety.

Handling nerves during the presentation

  • If you find that you are too uncomfortable to give audience members direct eye contact, a helpful technique is to look directly over the heads of the audience as this gives the impression of eye contact.
  • Try not to engage in nervous behaviours e.g. shifting your weight or fidgeting.
  • Remember that it’s unlikely that the audience knows that you are feeling nervous – you do not look as anxious as you feel.
  • Notice whether you are speaking too quickly as this tends to happen when nervousness increases. If you are, pause and then slow down.

Strong conclusion

Since the conclusion is the last section of your presentation the audience is more likely to remember it. Summarise the key points and lead into a clear concluding statement. For example, if your presentation was on the impact of social media on self-esteem you could list all the main points covered in the presentation and conclude “Therefore, from the amount of evidence and also from the quality of evidence, we have decided that social media is negatively/positively impacting self-esteem.”

Questions and answer session

The questions and answers session after the main presentation can be a source of anxiety as it is often difficult to predict what questions will be asked. But working within a group setting means that individually you do not have to know everything about the topic.

When an  audience member asks a question , the presentation moderator can refer a speaker who has the relevant knowledge to provide an answer. This avoids any hesitant pauses.

If you are answering group presentation questions:

  • Pause before answering- take the time to gather your thoughts and think about your answer
  • Make sure you answer the question- sometimes you may start providing more information than necessary. Keeping answers as concise as possible will help with this.
  • Ask the questioner for clarification if you do not understand- it’s better to ask rather than answering in a way that does not address the question.
  • You’re not expected to know everything- challenging questions will emerge and if you do not know the answer you can respond with: “That’s a really good question, I’m not certain so let me look into that.”

Ending the presentation

A good ending usually consists of the presentation moderator thanking the audience. If there is another group afterwards they should transition to the next group.

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SpeakUp resources

Starting a presentation in english: methods and examples.

  • By Jake Pool

introducing group in presentation

If you’re going to make it in the professional world, most likely you’ll have to give a presentation in English at some point. No reason to get nervous!

Most of the work involved lies in the introduction. You may or may not need an English presentation PPT file, your topic, audience, or time limit may vary, but a strong opening is a must no matter what! Everything that follows can build from the opening outline you present to your audience.

Let’s look at some guidelines for starting a presentation in English. If you can master this part, you’ll never have to worry about the rest!

Opening in a Presentation in English

While it’s important to have your entire presentation organized and outlined, planning and organization are especially important in the introduction. This is what will guide you through a clear and concise beginning. Let’s look at how to start a presentation with well-organized thoughts .

Introduction Outline

  • Introduce yourself and welcome everyone.
  • State the purpose of your presentation
  • Give a short overview of the presentation

As we say, it’s as easy as 1-2-3. (No need for a more detailed English presentation script!) Let’s examine the first step.

1. Introduce Yourself & Welcome Everyone

The self-introduction is your opportunity to make a good first impression. Be sure to open with a warm welcome and use language that is familiar and natural. Based on your audience, there are a few different expressions you can use to start your presentation.

If you’re presenting to coworkers who may already know you:

  • Hello, [name] here. I would like to thank you all for your time. As you may know, I [describe what you do/your job title] I look forward to discussing [topic] today.
  • Good morning/afternoon/evening everyone. Thank you for being here. For those who don’t know me, my name is [name], and for those who know me, hello again.

If you’re presenting to people you’ve never met:

  • Hello everyone, it’s nice to meet you all. My name is [name] and I am the [job/title].
  • Hello. Welcome to [event]. My name is [name] and I am the [job/title]. I’m glad you’re all here.

There are certainly more ways to make an introduction. However, it’s generally best to follow this format:

  • Start with a polite welcome and state your name.
  • Follow with your job title and/or the reason you’re qualified to speak on the topic being discussed.

2. State the Purpose of Your Presentation

Now that your audience knows who you are and your qualifications, you can state the purpose of your presentation. This is where you clarify to your audience what you’ll be talking about.

So, ask yourself, “ What do I want my audience to get from this presentation? ”

  • Do you want your audience to be informed?
  • Do you need something from your audience?
  • Do you want them to purchase a product?
  • Do you want them to do something for the community or your company?

With your goal in mind, you can create the next couple of lines of your presentation. Below are some examples of how to start.

  • Let me share with you…
  • I’d like to introduce you to [product or service]
  • Today I want to discuss…
  • I want to breakdown for you [topic]
  • Let’s discuss…
  • Today I will present the results of my research on [topic]
  • By the end of this presentation, you’ll understand [topic]
  • My goal is to explain…
  • As you know, we’ll be talking about…

When talking about the purpose of your presentation, stick to your goals. You purpose statement should be only one to three sentences. That way, you can give your audience a clear sense of purpose that sets them up for the rest of the presentation.

3. A Short Overview of the Presentation

The final step in starting your presentation is to give a short outline of what you’ll be presenting. People like a map of what to expect from a presentation.

It helps them organize their thoughts and gives a sense of order. Also, it lets the audience know why they’re listening to you. This is what you’ll use to grab their attention, and help them stay focused throughout the presentation.

Here are some examples of how you can outline your presentation:

  • Today, I’m going to cover… Then we’ll talk about… Lastly, I’ll close on…
  • We’re going to be covering some key information you need to know, including…
  • My aim with this presentation is to get you to… To do that we’ll be talking about…
  • I’ve divided my presentation into [number] sections… [List the sections]
  • Over the next [length of your presentation] I’m going to discuss…

That’s it! It’s as simple as 1-2-3. If you have a fear of public speaking or are not confident about presenting to a group of people, follow these three steps. It’s a simple structure that can get you off to a good start. With that in mind, there are other ways to bring your introduction to the next level too! Read on for bonus tips on how to really engage your audience, beyond the basics.

For a Strong Presentation in English, Engage your Audience

Presentations aren’t everyone’s strongest ability, and that’s OK. If you’re newer to presenting in English, the steps above are the basics to getting started. Once you’re more comfortable with presenting, though, you can go a step further with some extra tricks that can really wow your audience.

Mastering the skill of engaging an audience will take experience. Fortunately, there are many famous speakers out there you can model for capturing attention. Also, there are some common techniques that English-speakers use to gain an audience’s attention.

*How and when you use these techniques in your introduction is at your discretion, as long as you cover the 3 steps of the introduction outline that we discussed earlier.*

Do or say something shocking.

The purpose of shocking your audience is to immediately engage them. You can make a loud noise and somehow relate the noise to your presentation. Or, you can say, “ Did you know that… ” and follow with a shocking story or statistic. Either way, the objective is to create surprise to draw their attention.

Tell a story

Telling a story related to your presentation is a great way to get the audience listening to you.

You can start by saying, “ On my way to [location] the other day… ” or “ On my way here, I was reminded of… ” and then follow with a story. A good story can make your presentation memorable.

Ask your audience to take part

Sometimes a good introduction that captures attention will involve asking for help from the audience. You can ask the audience to play a quick game or solve a puzzle that’s related to your presentation. Also, you could engage the audience with a group exercise. This is a great way to get people involved in your presentation.

There are many more ways to engage the audience, so get creative and see what you can think up! Here are some resources that will help you get started.

Also, if you want to get better at public speaking (and help your English speaking too!), a great organization to know about is the Toastmasters . The organization is dedicated to helping you be a better speaker, and there are many local groups in America. They offer free lessons and events to help you master your English speaking, and also offer additional help to paying members.

The Takeaway

A presentation in English? No problem, as long as your introduction sets you up for success . Admittedly, this can be easier said than done. Native speakers and non-native speakers alike sometimes struggle with getting a good start on their English presentation. But the advice above can help you get the confidence you need to lay a good foundation for your next speech !

Jake Pool

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How to Organize Your Introduction for a Presentation [+ FREE Presentation Checklist]

May 1, 2018 | Business Professional English , Free Resource , Public Speaking & Presentations

How to Organize Your Introduction for a Presentation in English - Lesson

This lesson on how to organize your introduction for a presentation in English has been updated since its original posting in 2016 and a video has been added.

Getting ready to present in English? Here’s how to make sure your introduction for a presentation in English is successful.

But first… When you think about a presentation, I know you’re thinking about something like a TED video or a presentation at a conference. You’re thinking about a speech, with PowerPoint slides and a big audience.

But did you know we use the same skills when we share new information or ideas with our work colleagues? Or when we tell stories to our friends and family? The situation or speaking task may be different but we still use the same skills.

When presenting information or telling stories, we need to:

  • Capture a listener’s attention
  • Share information, ideas, or opinions
  • Give the important details
  • Make your information memorable
  • Get your audience (family, friends, colleagues or strangers) to agree, to take action, to change their mind, etc.

So today you’re going to learn how to take the first big step in your English presentation: how to start with a great introduction.

The introduction is the most important part of your presentation. It is the first impression you’ll make on your audience. It’s your first opportunity to get their attention. You want them to trust you and listen to you right away.

However, that first moment when you start to speak is often the hardest. Knowing how to best prepare and knowing what to say will help you feel confident and ready to say that first word and start your presentation in English.

Be sure to include these 5 things in your inroduction.

Lesson by Annemarie

How to Organize Your Introduction for a Presentation in English and Key Phrases to Use

Organize Your Introduction Correctly

Okay, first let’s focus on what you need to include in your English introduction. Think of this as your formula for a good introduction. Using this general outline for your introduction will help you prepare. It will also help your audience know who you are, why you’re an expert, and what to expect from your presentation.

Use this general outline for your next presentation:

  • Welcome your audience and introduce yourself
  • Capture their attention
  • Identify your number one goal or topic of presentation
  • Give a quick outline of your presentation
  • Provide instructions for how to ask questions (if appropriate for your situation)

Use Common Language to Make Your Introduction Easy to Understand

Great, now you have the general outline of an introduction for a speech or presentation in English. So let’s focus on some of the key expressions you can use for each step. This will help you think about what to say and how to say it so you can sound confident and prepared in your English presentation.

“The introduction is the most important part of your presentation. It is the first impression you’ll make on your audience. It’s your first opportunity to get their attention. You want them to trust you and listen to you right away.”

Welcome Your Audience & Introduction

It is polite to start with a warm welcome and to introduce yourself. Everyone in the audience will want to know who you are. Your introduction should include your name and job position or the reason you are an expert on your topic. The more the audience trusts you, the more they listen.

  • Welcome to [name of company or event]. My name is [name] and I am the [job title or background information].
  • Thank you for coming today. I’m [name] and I’m looking forward to talking with you today about [your topic].
  • Good morning/afternoon ladies and gentlemen. I’d like to quickly introduce myself. I am [name] from [company or position]. (formal)
  • On behalf of [name of company], I’d like to welcome you today. For those of you who don’t already know me, my name is [name] and I am [job title or background]. (formal)
  • Hi everyone. I’m [name and background]. I’m glad to be here with you today. Now let’s get started. (informal)

Capture Their Attention

For more information about how to best capture your audience’s attention and why, please see the next session below. However, here are a few good phrases to get you started.

  • Did you know that [insert an interesting fact or shocking statement]?
  • Have you ever heard that [insert interesting fact or shocking statement]?
  • Before I start, I’d like to share a quick story about [tell your story]…
  • I remember [tell your story, experience or memory]…
  • When I started preparing for this talk, I was reminded of [tell your story, share your quote or experience]…

Identify Your Goal or Topic of Presentation

At this stage, you want to be clear with your audience about your primary topic or goal. Do you want your audience to take action after your talk? Is it a topic everyone is curious about (or should be curious about)? This should be just one or two sentences and it should be very clear.

  • This morning I’d like to present our new [product or service].
  • Today I’d like to discuss…
  • Today I’d like to share with you…
  • What I want to share with you is…
  • My goal today is to help you understand…
  • During my talk this morning/afternoon, I’ll provide you with some background on [main topic] and why it is important to you.
  • I will present my findings on…
  • By the end of my presentation, I’d like for you to know…
  • I aim to prove to you / change your mind about…
  • I’d like to take this opportunity to talk about…
  • As you know, this morning/afternoon I’ll be discussing…

Outline Your Presentation

You may have heard this about presentations in English before:

First, tell me what you’re going to tell me. Then tell me. And finally, tell me what you told me.

It sounds crazy and weird, but it’s true. This is how we structure presentations in English. So today we’re focusing on the “First, tell me what you’re going to tell me” for your introduction. This means you should outline the key points or highlights of your topic.

This prepares your listens and helps to get their attention. It will also help them follow your presentation and stay focused. Here are some great phrases to help you do that.

  • First, I’m going to present… Then I’ll share with you… Finally, I’ll ask you to…
  • The next thing I’ll share with you is…
  • In the next section, I’ll show you…
  • Today I will be covering these 3 (or 5) key points…
  • In this presentation, we will discuss/evaluate…
  • By the end of this presentation, you’ll be able to…
  • My talk this morning is divided into [number] main sections… First, second, third… Finally…

On Asking Questions

You want to be sure to let you audience know when and how it is appropriate for them to ask you questions. For example, is the presentation informal and is it okay for someone to interrupt you with a question? Or do you prefer for everyone to wait until the end of the presentation to ask questions?

  • If you have any questions, please don’t hesitate to interrupt me. I’m happy to answer any questions as we go along.
  • Feel free to ask any questions, however, I do ask that you wait until the end of the presentation to ask.
  • There will be plenty of time for questions at the end.
  • Are there any questions at this point? If not, we’ll keep going.
  • I would be happy to answer any questions you may have now.

Capture Your Audience’s Attention

Do you feel unsure about how to capture the attention of your audience? Don’t worry! Here are some common examples used in English-speaking culture for doing it perfectly!

Two of the most famous speakers in the English-speaking world are Steve Jobs and Oprah Winfrey. While Steve Jobs is no longer living, people still love to watch his speeches and presentations online. Oprah is so famous that no matter what she does, people are excited to see her and listen to her.

BUT, if you listen to a speech by Steve Jobs or Oprah Winfrey,  they still  work  to get your attention!

The don’t start with a list of numbers or data. They don’t begin with a common fact or with the title of the presentation. No – they do much more.

From the moment they start their speech, they want you to listen. And they find interesting ways to get your attention. In his most famous speeches, Steve Jobs often started with a personal story. And Oprah often starts with an inspiring quote, a motivational part of a poem, or a personal story.

These are all great ways to help your audience to listen to you immediately – whether your presentation is 3 minutes or 20 minutes.

Here’s how you can do it.

Like Steve Jobs or Oprah Winfrey, start with a:

  • Personal story or experience
  • Motivational quote or line from a poem or book
  • Joke (be careful with this – make sure it translates easily to everyone in the audience!)
  • Shocking, bold statement (Think of Steve Jobs’ quote: “ Stay hungry. Stay Foolish .”)
  • Rhetorical question ( =a question that you don’t want an answer to; the focus is to make someone think)

And finally, consider audience participation. Ask a question and get your audience to respond by raising hands.

Get the complete Presentations in English Series:

Part 1: How to Prepare for Your Presentation in English

Part 2: How to Start with a Great Introduction in Your Presentation

Part 3:  How to Organize Your Presentation in English

Part 4:  How to End Your Presentation Powerfully

As I mentioned in the video, I have two question for you today:

  • What is the best introduction you’ve ever heard? Have you watched a TED Talk or a presentation on YouTube with a great introduction? Tell me about it. What do you think was great about the introduction?
  • What frightens you the most about preparing your introduction in a presentation? Share your concerns with me so I can help you overcome any challenges you have.

Be sure to share in the comments below to get feedback from me and to learn from others in the Confident English Community.

Have a great week! ~ Annemarie

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guest

Thank you, Annemarie. thanks for the generosity of sharing useful and systemative information and content.

Dharitri karjee

This is really a very informative message thank you.. And it’s help me a lot

yami

hi thank you for this It was helpful. You used simple english that i understood well.

Gassimu Zoker

How to start with a great presentation on composition

Anshika Abhay Thakur

Thankyou for the information . It was much helpful . I will definitely use this information in my presentation 🤗

Thang Sok

Hi, I am Thang Sok Do you have a Sample presentation?

Khadija

This was helpful but can you please tell me how to start a presentation in college because this is for work in a company. My presentation is on laboratory skills and all that

Anum

Its informative

Yasin Hamid

Thank you for this video! I’ve learned quite a lot and will want to use all these knowledge in presenting my thesis proposal in 2 months. About your question no. 2, I’d just like to share that the mere fact of presenting in front of many respected professionals makes me already nervous and shaky even if i have studied everything about my presentation. What do you think should i do to deal with my concern?

martineromy940

Could you give me advise, how to start learning English for beginner.How to prepare presentation on any topic and how to make interesting..

Pratik

Thank u so much for valuable advice. Definitely I will used this in my presentation!!

Farangiz

Thank you very much for these kind of useful advice. I hope my first presentation will be exciting for the audience.Your video is helping me again thanks a lot 😊

yumna

hi, i’m B.COM student and I have to prepare presentation about identifying business opportunities. How to start and an attractive attention to my audience.. Please Help me…

Nancy Tandui

very nise and educative piece of information thank you nancy nairobi kenya

kanishka mishra

i am starting a video speech shooting in night about a famouse person how do i start my speech with a good intro.

Kate

Hi again how do you do a introduction goodbye

kate

Hi i do not know what you are talking about

Annemarie

Hi Kate, I’m sorry to hear you’re not sure about the content. I recommend reviewing the video carefully if you haven’t already. Is there something specific you have a question about?

Tooba

thanks a lot for guiding in such an easier way.

Amit

Your write-up on introduction helped a lot, thank you Annemarie. I work for cross-geography team and greetings get lengthy as timezones are different e.g. “Good evening to those joining from US office and good morning to colleagues from India office”. I replaced that with “Thank you everyone for joining”. Is it okay?

Hi Amit, I’m so glad it was helpful. As for your greeting, both of your options are perfectly appropriate and friendly.

znb

How to introduce group members in online presentation?

Great question! I’d love to use that for a future Confident English lesson.

zarsha

its amazing. i can’t explain in wording. this material helping me a lot. i am so happy after use this website . its make easy for me preparing my presentation more interesting. i am thankful too u.

jinah

thanks! i use your materials to teach my students(clinets) how to prepare a presentation. is it ok to use them on my materials?

Matangi

Hi! I am a student from the USP from Tuvaluan and i take CEE45 so our assessment 2 is to prepared a group presentation and we presented in school. so need your help for how to start an attractive introduction to my teacher and my fellow students, they already kwow me.

Zainab

Thank you.. very helpful

Moataz Saleh

Very useful

Taha

It was very use Gul for or presentations

Gaman Aryal

Hi. I am a 1st year BIT student and I have to prepare a presentation on 3D Printing. how to start an attractive introduction to my teachers, when they already know about me? Can you please help me out? Thank you.

Andrew

I just took 1st place for my paper that I presented at an international students conference. I used a lot of your techniques to improve my speech and I have no words to say how grateful I am to you. Keep up the good work!

😲WOW!! That’s awesome, Andrew. 🙌Congratulations on your presentation. What a wonderful response to your hard work. I’d love to know what you presentation was about. And thank you for sharing your new here. I’m thrilled to know that my techniques were helpful to you.

The title of the presentation was “Handling burnout: A study regarding the the influence of job stressors over military and civilian personel”. I can sent you my paper through email if you would like to see it.

Hi Andrew, what a fascinating topic. And it’s interesting because I just had a newspaper reporter interview me about burnout as a small business owner. Must be a hot topic. 🙂 And sure, I’d love to see it.

Mariya

🔥❤ too goodd

Helia

Hello Annemarie, Thank you so much for one of the best content on the English presentation, I’ve seen. I have a question: Is it impolite or informal to start the presentation without a greeting? I’m asking this question because I’ve seen a lot of TEDTalks and in only a few of them, they greet the audience and in most of it, they quickly go to the “CAPTURING the ATTENTION” with numbers and pictures. I would be so thankful if you could answer this question as soon as possible, my presentation is so close. Best regards, Helia

Hi Helia, What a great question. It has definitely become more common to skip the greeting and go straight to capturing the attention of the audience and you’re right that we often see this in TED talks. I would say it’s best to know your audience and what might be expected. For example, at more formal, traditional conferences or lecture, it might be more appropriate to start with a welcome. I prefer to welcome/thank my audience quickly at the start when I give presentations. A welcome can be very brief, just one sentence, and then you can quickly go into …  Read more »

Vivek Shukla

Hi Annemarie I would like to thank you for giving such types of presentation skills but I have a question can you give me some idea about vote of thinks.

I’m glad the lessons are helpful to you. Could you clarify what you mean by ‘vote of thinks?’ I’m not sure I understand that.

Bello

Please can you give me some idea about vote of thanks

Could you clarify what you’re asking for, Bello?

Amrit

Thanks a lot

Glad it was helpful!

tadla

it is agood i learn alot from this english class

Radha Mohan

Hello.i would like to thank you for giving these beautiful tips to start a presentation.This article helped me a lot.

That’s great, Radha. Glad to hear it.

Mithun Kumar

Thanks for your article. It’s simply for interpersonal skill development.

You’re welcome, Mithun. Glad to know it was helpful.

Swetha

Hi Annemarie . Thank you so much for giving such helpful guildelines it’s really gonna help me

I’m glad it’s helpful, Swetha! 🙂

dawharu boro

thank you for help me

You’re very welcome!

Tom

Hi Anne Marie, i ‘m from Catalonia and i came across with your site only by chance and i think it’gonna be so helpful for me to pass the next test for c1 level. Several weeks ago i did some rehersals with my presentation and i was so nervous and terrified about what was expected from me.

Some tips in your youtube channel are so cool !!! Thank you.

Hi Tom, I’m thrilled you’ve found this site in your preparations for your English exam and am glad to know it’s helpful! Best of luck as you continue to prepare.

Fatima

Hi Annemarie Thanks it’s so useful to develop presentation skill. Fatima

You’re very welcome, Fatima! I’m glad it was helpful.

Dzmitry

Awesome, especially this simple and clear motto: “First, tell me what you’re going to tell me. Then tell me. And finally, tell me what you told me.” This three sentences exactly explain the content you need to create a memorable presentation.

Hi Dzmitry,

Yes, I’ve always loved that simple motto on how to do a presentation. 🙂 It’s so easy to remember and tells you exactly what to do.

Mahbub

hello I need to introduce myself to language center. i am going to learn Danish Language and i want to introduce myself to them and i am little bit nervous because my grammar is not good at that level.so will you please guide me how to introduce myself to them with an example. i did go through your examples but that is for professionals and i am just a student (Graduate). I don’t have any experience . Please guide me how to do it.

Navin Shivram SS

I was in a confused state about starting a conversation and proceeding in it but when I read the guidelines you mentioned above I became confident. thank you for your innumerable ………….

Salma

Thank you so much…… it’s an excellent topic, and it helped me a lot

I’m so glad this was helpful to you! Thank you for sharing.

rebecca

hi annemarie i have a few questions about a speech i have to make a englishi speech of what i want to become can you help me?

Hi Rebecca,

Thank you for the question. I have several lessons on the topic of presentations in English . However, for personal assistance with English or presentations, I only do that through my one-on-one classes .

Shalini Tripathi

thank you so much…… it’s really helpful for me….

You’re very welcome, Shalini.

Mohammed Zaid ameen

Thanks its really nice to develop the presentation skills

Awesome. I’m glad it was helpful to you, Mohammed.

dinesh dhakar

I have to give a demo on one of your programs next week. I would like you to check my self introduction – Good afternoon everyone and thank you for all of your presence. Before we get into the session I would like to quickly introduce myself. My name is Dinesh . I am working as a Pharmaceutical sale and promotion of the brands for Arrient Healthcare. I am in this filed for the past ten years. Before becoming trainer I worked as a medical representatives for different pharma company . I am highly interested in learning from people and …  Read more »

Monica

Please ignore my previous comment. Yea the demo was a success. So hereafter I will say”I have been in this field for the past four years. Actually I worked for different consultancies so I didn’t include an article there.

Monica

I have to give a demo on one of your programs next week. I would like you to check my self introduction – Good afternoon everyone and thank you for all of your presence. Before we get into the session I would like to quickly introduce myself. My name is Monica. I am working as a Soft Skill Trainer at Synergy School of Business Skills. I am in this filed for the past four years. Before becoming trainer I worked as a Recruiter for different job consultancy. I am highly interested in learning from people and I think teaching/training is …  Read more »

Thank you for sharing your example! One note: “I am in this field for the past four years.” –> Don’t forget, when we’re talking about something that started in the past and continues to now, we use the present perfect. How might you change this sentence to fix the grammar?

Also, we want to add an article to, “… I worked as a recruiter for [a] different job consultancy.”

I wish you much success in your demo this week! Best, Annemarie

Yea the demo was a success! So hereafter I will say”I have been for the past four years. Actually I worked for different consultancies.

Fadia

I like it but I think capturing their attention is the most difficult part in preparing a presentation. From my little experience, I used to talk about something out of the scope of the presentation in order to grasp their attention. For example, I had a presentation about medical terminology and its parts (suffix, prefix —). So I provided example which is Ultra Violet then I talked about the ultraviolet in the sun and Vitamin D deficiency. They liked the talk because it is very important to them and by this topic I captured their attention more and more.

Hello Fadia, I’m sorry I’m so late in responding to your comment! I agree with you: capturing attention is very challenging to do. It requires understanding your audience, knowing what is important to them, and how to connect with them. In English-speaking culture, we often connect by telling a story or showing we understand a problem the audience has. I think you’re exactly right to talk about something that is maybe “off topic” or out of the scope of the presentation, as you said, to get their attention first. It sounds like you did a great job in your experience!! …  Read more »

sonam

hi there it was great going through your enlightening presentation skills however i would be even more delighted if you put some quotes for various PPT’s which will give us an instant ideas during the adhoc PPT like myself…just a suggestion.

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5 Powerful Group Presentation Examples + Guide to Nail Your Next Talk

Leah Nguyen • 04 April, 2024 • 8 min read

A group presentation is a chance to combine your superpowers, brainstorm like mad geniuses, and deliver a presentation that’ll have your audience begging for an encore.

That’s the gist of it.

It can also be a disaster if it’s not done right. Fortunately, we have awesome group presentation examples to help you get the hang of it💪.

Table of Contents

What is a good group presentation, #1. delivering a successful team presentation, #2. athletetrax team presentation, #3. bumble – 1st place – 2017 national business plan competition, #4. 2019 final round yonsei university, #5. 1st place | macy’s case competition, bottom line, frequently asked questions, tips for audience engagement.

  • Manager your timing in presentation better
  • Learn to introduce team member now

Alternative Text

Start in seconds.

Get free templates for your next interactive presentation. Sign up for free and take what you want from the template library!

Group presentation example

Here are some key aspects of a good group presentation:

• Organisation – The presentation should follow a logical flow, with a clear introduction, body, and conclusion. An outline or roadmap shown upfront helps guide the audience.

• Visual aids – Use slides, videos, diagrams, etc. to enhance the presentation and keep it engaging. But avoid overly packed slides with too much text. For the sake of convenience of quickly sharing the content, you can attach a QR code directly in your presentation using slides QR code generator for this goal.

• Speaking skills – Speak clearly, at an appropriate pace and volume. Make eye contact with the audience. Limit filler words and verbal tics.

• Participation – All group members should contribute to the presentation in an active and balanced way. They should speak in an integrated, conversational manner. You can also gather attention from your audience by using different interactive features, including spinner wheel live word clouds , live Q&A , online quiz creator and survey tool , to maximize engagement.

🎉 Choose the best Q&A tool with AhaSlides

• Content – The material should be relevant, informative, and at an appropriate level for the audience. Good research and preparation ensure accuracy.

• Interaction – Involve the audience through questions, demonstrations, polls , or activities. This helps keep their attention and facilitates learning.

• Time management – Stay within the allotted time through careful planning and time checks. Have someone in the group monitor the clock.

• Audience focus – Consider the audience’s needs and perspective. Frame the material in a way that is relevant and valuable to them.

• Conclusion – Provide a strong summary of the main points and takeaways. Leave the audience with key messages they’ll remember from your presentation.

🎊 Tips: Icebreaker games | The secret weapon for connecting a new group

Present in powerful and creative visual

Engage your audience in real-time. Let them imprint your presentation in their head with revolutionising interactive slides!

Best Group Presentation Examples

To give you a good idea of what a good group presentation is, here are some specific examples for you to learn from.

The video provides helpful examples and recommendations to illustrate each of these tips for improving team presentations.

The speaker recommends preparing thoroughly as a team, assigning clear roles to each member, and rehearsing multiple times to deliver an effective team presentation that engages the audience.

They speak loudly and clearly, make eye contact with the audience, and avoid reading slides word for word.

The visuals are done properly, with limited text on slides, and relevant images and graphics are used to support key points.

The presentation follows a logical structure, covering the company overview, the problem they are solving, the proposed solution, business model, competition, marketing strategy, finances, and next steps. This makes it easy to follow.

The presenters speak clearly and confidently, make good eye contact with the audience, and avoid simply reading the slides. Their professional demeanor creates a good impression.

They provide a cogent and concise answer to the one question they receive at the end, demonstrating a good understanding of their business plan.

This group nails it with a positive attitude throughout the presentation . Smiles show warmness in opposition to blank stares.

The team cites relevant usage statistics and financial metrics to demonstrate Bumble’s growth potential. This lends credibility to their pitch.

All points are elaborated well, and they switch between members harmoniously.

This group presentation shows that a little stutter initially doesn’t mean it’s the end of the world. They keep going with confidence and carry out the plan flawlessly, which impresses the judging panel.

The team provides clear, supported responses that demonstrate their knowledge and thoughtfulness.

When answering the questions from the judge, they exchange frequent eye contact with them, showing confident manners.

🎉 Tips: Divide your team into smaller groups for them to practice presenting better!

In this video , we can see instantly that each member of the group takes control of the stage they present naturally. They move around, exuding an aura of confidence in what they’re saying.

For an intricate topic like diversity and inclusion, they made their points well-put by backing them up with figures and data.

🎊 Tips: Rate your presentation by effective rating scale tool , to make sure that everyone’s satisfied with your presentation!

We hope these group presentation examples will help you and your team members achieve clear communication, organisation, and preparation, along with the ability to deliver the message in an engaging and compelling manner. These factors all contribute to a good group presentation that wow the audience.

More to read:

  • 💡 10 Interactive Presentation Techniques for Engagement
  • 💡 220++ Easy Topics for Presentation of all Ages
  • 💡 Complete Guide to Interactive Presentations

What is a group presentation?

A group presentation is a presentation given by multiple people, typically two or more, to an audience. Group presentations are common in academic, business, and organisational settings.

How do you make a group presentation?

To make an effective group presentation, clearly define the objective, assign roles among group members for researching, creating slides, and rehearsing, create an outline with an introduction, 3-5 key points, and a conclusion, and gather relevant facts and examples to support each point, include meaningful visual aids on slides while limiting text, practice your full presentation together and provide each other with feedback, conclude strongly by summarising key takeaways.

Leah Nguyen

Leah Nguyen

Words that convert, stories that stick. I turn complex ideas into engaging narratives - helping audiences learn, remember, and take action.

Tips to Engage with Polls & Trivia

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From Qualitative to Quantitative | Online Guide to Combining Q&A with Other Research Methods Article

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How to Give a Group Presentation

Taylor Risner

Presenting with other speakers comes with inherent challenges that can be tough to navigate. In the end, the presentation is only as good as its weakest speaker, so the pressure is on to make sure that everyone participating brings their A-game to help the presentation shine. We’ve found ourselves in hundreds of group presentation settings for conference speeches, sales proposals, pitch decks, and product demos. This article shares our key learnings and provides best practices to help you deliver an excellent co-presentation.

Team Dynamics 

The best first step to take for a group presentation is identifying roles for the participants. The most important role to identify is the lead role or team captain. Whoever is leading the presentation will ultimately be responsible for a number of tasks that are critical to the success of the presentation. 

Team Lead/Captain

The team lead/captain is responsible for starting the presentation. This means they need to ensure there is an attention grab early in the presentation to captivate the audience. They’ll also be responsible for setting the context and introducing the team. The team lead should be highly personable, charismatic, and trustworthy to set the presentation off on the right foot. 

After starting the presentation, the audience will naturally understand the individual’s leadership role and it will make the most sense to them for the leader to also finish the presentation. So we recommend for the best natural flow, that the team lead also finish the presentation. This means they’ll be responsible for wrapping up the key points discussed and to ensure the audience walks away with clear takeaways. 

If the presentation allows for questions, the team lead should also be designated as the key spokesperson to field the questions and either answer them or route them to the appropriate members on the team. 

Other Roles

It’s also important to identify other roles on the team if applicable. In some presentations it may make sense to split up speakers by core topic or their area of expertise. In other cases, it may be most appropriate to have a single speaker outside of the team lead and then have a few supporting members for the Q&A session. Or perhaps you’re delivering a data-heavy presentation and it’s best to bring in an analyst to speak over the data insights. 

Another key point to remember is that the more speakers you include, typically the longer the presentation will take. So be sure to factor in the time allowed for the presentation into how you structure your team dynamics. 

The real point is that there is no exact template for who should speak when. Our simple recommendation is to always identify a team leader for every group presentation, and then from there, build a presentation team that best fits your subject matter, audience, format, and time allowed. 

Preparation  

The importance of preparing and practicing for the upcoming presentation cannot be understated. Preparation is critical to make sure that everyone knows their role, understands transitions, knows who is speaking before and after them, understands the flow of the narrative, and is comfortable with how they’ll handle the room layout plus technology. 

group presentation skills co-speakers co-presentation practice

Understand your Role

As discussed in the team dynamics section above, everyone must first understand their role so that they understand what content they will be speaking about and if they have to assume any other duties such as introductions, answering questions, opening and closing the presentation, speaking about data, etc. 

Align on the Narrative

Once everyone is clear about their roles, the next step in preparation is understanding the flow of the narrative. Each team member may have a different idea in mind on what message they want to deliver with the presentation. Needless to say, if you have four speakers all communicating a different message, the presentation will flop and the key points will be mute. Co-presenters should discuss the narrative end-to-end and align on how their speaking points tie into that core message. Getting everyone on the same page can help to deliver a seamless and powerful narrative. 

Practice Transitions

Once you have roles defined and a consistent narrative established, co-speakers should work on their transitions. Speakers cannot simply rehearse their own material and forget about the handoffs. This is a sure-fire way to lose the audience’s trust and attention. There are many ways to prepare for transitions, but we have two favorite best practices. 

The first is the review preview method. This approach means the speaker takes 1-2 sentences to recap what they just discussed and then another 1-2 sentences to preview the material that the next speaker will cover. As a team, presenters should run through this method together to make sure that their speaking points flow together and team members do their best to set the next speaker up for success. 

The second best practice to prepare for transitions is to use speaker notes . Speaker notes can be an effective tool to include directions for the presentation directly on the slides. You can prepare by leaving clues for yourself on how to transition between slides, what is coming next, and who you are handing off the speaking floor to. 

Prepare for Room Layout + Technology

The last step to preparing for a joint presentation is making sure everyone understands how the room layout and technology will affect the presentation. For example, if a large screen is centered behind the stage, it will make the most sense to group speakers together on both sides based on who is speaking in what sequence. Also, if there is only going to be one handheld microphone that will need to be planned for vs. everyone having their own clip on microphone. Almost every setting we’ve presented in has had a different room and technology layout, so this one is difficult to prepare for. Our recommendation is to at least reach out and ask for specific details so that your team can do their best to prepare accordingly. 

Live During the Presentation 

After you’ve aligned on team dynamics and prepared thoroughly, it’s time to execute. We’ve learned a few lessons that are important to keep in mind. 

Connect With the Other Speakers

When you present with other speakers, the audience will want to understand how you connect with each other. They’ll be wondering how you know each other, what your current relationship is, if you get along, how your personalities differ, and more. To engage the audience, don’t be afraid to put your relationships on display and use storytelling to help them better understand how all the speakers are connected. This will help the audience to better emphasize with your presentation. 

Stay Focused While Others Present

This tip should go without saying, but it’s harder to follow than you’d think. You may start thinking ahead about what you’re going to say and end up looking like you’re dozing off and uninterested in what your co-presenters have to say. The audience will pick up on these visual cues. If you don’t appear to be interested, then why should they be? So remember to focus when others are speaking and look interested in what they have to say. Head nods, laughs, verbal reinforcement… you get the gist. 

Establish Your Own Voice but Don’t Hog the Mic

Co-presentations really thrive when each speaker shows off their skills and knowledge in their own way. So it’s important that every speaker is confident in their speaking abilities and establishes their own voice. However, this combined with passion about the presentation topic can lead an individual to hog the microphone. There’s nothing worse than having to rush through your section in two minutes because the speaker before you went 15 minutes over their allotted time. So be considerate of your co-speakers and let your voice shine within the time that you’re allowed. 

In Conclusion

As you and your co-speakers gear up for your next big speech or proposal, remember these simple guidelines. Establish team dynamics, practice the speech end-to-end as if it were live, and be conscious of your effect on the presentation both when you’re speaking and listening. Best of luck! 

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Home Blog Presentation Ideas How to Start a Presentation: 5 Strong Opening Slides and 12 Tricks To Test

How to Start a Presentation: 5 Strong Opening Slides and 12 Tricks To Test

Cover image of a How to Start a Presentation article with an illustration of a presenter giving a speech.

Knowing how to start a presentation is crucial: if you fail to capture the audience’s attention right off the bat, your entire presentation will flop. Few listeners will stick with you to the end and retain what you have told.

That is mildly unpleasant when you are doing an in-house presentation in front of your colleagues. But it can become utterly embarrassing when you present in front of larger audiences (e.g., at a conference) or worse – delivering a sales presentation to prospective customers.

Here is how most of us begin a presentation: give an awkward greeting, thank everyone for coming, clear our throats, tap the mic, and humbly start to mumble about our subject. The problem with such an opening performance? It effectively kills and buries even the best messages.

Table of Contents

  • The Classic Trick: Open a Presentation with an Introduction
  • Open a Presentation with a Hook
  • Begin with a Captivating Visual
  • Ask a “What if…” Question
  • Use the Word “Imagine”
  • Leverage The Curiosity Gap
  • The Power of Silence
  • Facts as Weapons of Communication
  • Fact vs. Myths
  • The Power of Music
  • Physical Activity
  • Acknowledging a Person

How to Start a PowerPoint Presentation The Right Way

Let’s say you have all of your presentation slides polished up (in case you don’t, check our quick & effective PowerPoint presentation design tips first). Your presentation has a clear storyline and agenda. Main ideas are broken into bite-sized statements for your slides and complemented with visuals. All you have left is to figure out how you begin presenting.

The best way is to appeal to and invoke certain emotions in your audience – curiosity, surprise, fear, or good old amusements. Also, it is recommended to present your main idea in the first 30 seconds of the presentation. And here’s how it’s done.

1. The Classic Trick: Open a Presentation with an Introduction

Bio Slide design for PowerPoint

When you don’t feel like reinventing the wheel, use a classic trick from the book – start with a quick personal introduction. Don’t want to sound as boring as everyone else with your humble “Hi, I’m John, the head of the Customer Support Department”? Great, because we are all about promoting effective presentation techniques (hint: using a dull welcome slide isn’t one of them).

Here’s how to introduce yourself in a presentation the right way.

a. Use a link-back memory formula

To ace a presentation, you need to connect with your audience. The best way to do so is by throwing in a simple story showing who you are, where you came from, and why your words matter.

The human brain loves a good story, and we are more inclined to listen and retain the information told this way. Besides, when we can relate to the narrator (or story hero), we create an emotional bond with them, and, again – become more receptive, and less skeptical of the information that is about to be delivered.

So here are your presentation introduction lines:

My name is Joanne, and I’m the Head of Marketing at company XYZ. Five years ago I was working as a waitress, earning $10/hour and collecting rejection letters from editors. About ten letters every week landed to my mailbox. You see, I love words, but decent publisher thought mine were good enough. Except for the restaurant owner. I was very good at up-selling and recommending dishes to the customers. My boss even bumped my salary to $15/hour as a token of appreciation for my skill. And this made me realize: I should ditch creative writing and focus on copywriting instead. After loads of trial and error back in the day, I learned how to write persuasive copy. I was no longer getting rejection letters. I was receiving thousands of emails saying that someone just bought another product from our company. My sales copy pages generated over $1,500,000 in revenue over last year. And I want to teach you how to do the same”

b. Test the Stereotype Formula

This one’s simple and effective as well. Introduce yourself by sharing an obvious stereotype about your profession. This cue will help you connect with your audience better, make them chuckle a bit, and set a lighter mood for the speech to follow.

Here’s how you can frame your intro:

“My name is ___, and I am a lead software engineer at our platform [Your Job Title]. And yes, I’m that nerdy type who never liked presenting in front of large groups of people. I would rather stay in my den and write code all day long. [Stereotype]. But hey, since I have mustered enough courage…let’s talk today about the new product features my team is about to release….”

After sharing a quick, self-deprecating line, you transition back to your topic, reinforcing the audience’s attention . Both of these formulas help you set the “mood” for your further presentation, so try using them interchangeably on different occasions.

2. Open a Presentation with a Hook

Wow your audience straight off the bat by sharing something they would not expect to hear. This may be one of the popular first-time presentation tips but don’t rush to discard it.

Because here’s the thing: psychologically , we are more inclined to pay attention whenever presented with an unexpected cue. When we know what will happen next – someone flips the switch, and lights turn on – we don’t really pay much attention to that action.

But when we don’t know what to expect next – e.g., someone flips the switch and a bell starts ringing – we are likely to pay more attention to what will happen next. The same goes for words: everyone loves stories with unpredictable twists. So begin your presentation with a PowerPoint introduction slide or a line that no one expects to hear.

Here are a few hook examples you can swipe:

a. Open with a provocative statement

It creates an instant jolt and makes the audience intrigued to hear what you are about to say next – pedal back, continue with the provocation, or do something else that they will not expect.

TED.com Jane McGonigal Ted Talk - This Game Will Give You 10 Years of Life

“You will live seven and a half minutes longer than you would have otherwise, just because you watched this talk.”

That’s how Jane McGonigal opens one of her TED talks . Shocking and intriguing, right?

b. Ask a rhetorical, thought-provoking question

Seasoned presenters know that one good practice is to ask a question at the beginning of a presentation to increase audience engagement. Rhetorical questions have a great persuasive effect – instead of answering aloud, your audience will silently start musing over it during your presentation. They aroused curiosity and motivated the audience to remain attentive, as they did want to learn your answer to this question.

To reinforce your message throughout the presentation, you can further use the Rhetorical Triangle Concept – a rhetorical approach to building a persuasive argument based on Aristotle’s teachings.

c. Use a bold number, factor stat

A clean slide with some mind-boggling stat makes an undeniably strong impact. Here are a few opening statement examples you can use along with your slide:

  • Shock them: “We are effectively wasting over $1.2 billion per year on producing clothes no one will ever purchase”
  • Create empathy: “Are you among the 20% of people with undiagnosed ADHD?”
  • Call to arms: “58% of marketing budgets are wasted due to poor landing page design. Let’s change this!”
  • Spark curiosity: “Did you know that companies who invested in speech recognition have seen a 13% increase in ROI within just 3 years?”

3. Begin with a Captivating Visual

Compelling visuals are the ABC of presentation design – use them strategically to make an interesting statement at the beginning and throughout your presentation. Your first presentation slide can be text-free. Communicate your idea with a visual instead – a photo, a chart, an infographic, or another graphics asset.

Visuals are a powerful medium for communication as our brain needs just 13 milliseconds to render what our eyes see, whereas text comprehension requires more cognitive effort.

Relevant images add additional aesthetic appeal to your deck, bolster the audience’s imagination, and make your key message instantly more memorable.

Here’s an intro slide example. You want to make a strong presentation introduction to global pollution.  Use the following slide to reinforce the statement you share:

Our Iceberg Is Melting Concept with Penguins in an Iceberg

“Seven of nine snow samples taken on land in Antarctica found chemicals known as PFAs, which are used in industrial products and can harm wildlife”

Source: Reuters

4. Ask a “What if…” Question

The “what if” combo carries massive power. It gives your audience a sense of what will happen if they choose to listen to you and follow your advice.  Here are a few presentations with starting sentences + slides to illustrate this option:

What if example with an Opening Slide for Presentation

Alternatively, you can work your way to this point using different questions:

  • Ask the audience about their “Why.” Why are they attending this event, or why do they find this topic relevant?
  • Use “How” as your question hook if you plan to introduce a potential solution to a problem.
  • If your presentation has a persuasion factor associated, use “When” as a question to trigger the interest of the audience on, for example, when they are planning to take action regarding the topic being presented (if we talk about an inspirational presentation).

What if technique analysis for a Financial topic

5. Use the Word “Imagine”

“Imagine,” “Picture This,” and “Think of” are better word choices for when you plan to begin your presentation with a quick story.

Our brain loves interacting with stories. In fact, a captivating story makes us more collaborative. Scientists have discovered that stories with tension during narrative make us:

  • Pay more attention,
  • Share emotions with the characters and even mimic the feelings and behaviors of those characters afterward.

That’s why good action movies often feel empowering and make us want to change the world too. By incorporating a good, persuasive story with a relatable hero, you can also create that “bond” with your audience and make them more perceptive to your pitch – donate money to support the cause; explore the solution you are offering, and so on.

6. Leverage The Curiosity Gap

The curiosity gap is another psychological trick frequently used by marketers to solicit more clicks, reads, and other interactions from the audience. In essence, it’s the trick you see behind all those clickbait, Buzzfeed-style headlines:

Curiosity Gap example clickbait Buzzfeed

Not everyone is a fan of such titles. But the truth is – they do the trick and instantly capture attention. The curiosity gap sparks our desire to dig deeper into the matter. We are explicitly told that we don’t know something important, and now we crave to change that. Curiosity is an incredibly strong driving force for action – think Eve, think Pandora’s Box.

So consider incorporating these attention grabbers for your presentation speech to shock the audience. You can open with one, or strategically weave them in the middle of your presentation when you feel like your audience is getting tired and may lose their focus.

Here’s how you can use the curiosity gap during your presentation:

  • Start telling a story, pause in the middle, and delay the conclusion of it.
  • Withhold the key information (e.g., the best solution to the problem you have described) for a bit – but not for too long, as this can reduce the initial curiosity.
  • Introduce an idea or concept and link it with an unexpected outcome or subject – this is the best opening for a presentation tip.

7. The Power of Silence

What would you do if you attended a presentation in which the speaker remains silent for 30 seconds after the presentation starts? Just the presenter, standing in front of the audience, in absolute silence.

Most likely, your mind starts racing with thoughts, expecting something of vital importance to be disclosed. The surprise factor with this effect is for us to acknowledge things we tend to take for granted.

It is a powerful resource to introduce a product or to start an inspirational presentation if followed by a fact.

8. Facts as Weapons of Communication

In some niches, using statistics as the icebreaker is the best method to retain the audience’s interest.

Say your presentation is about climate change. Why not introduce a not-so-common fact, such as the amount of wool that can be produced out of oceanic plastic waste per month? And since you have to base your introduction on facts, research manufacturers that work with Oceanic fabrics from recycled plastic bottles .

Using facts helps to build a better narrative, and also gives leverage to your presentation as you are speaking not just from emotional elements but from actually recorded data backed up by research.

9. Fact vs. Myths

Related to our previous point, we make quite an interesting speech if we contrast a fact vs. a myth in a non-conventional way: using a myth to question a well-accepted fact, then introducing a new point of view or theory, backed on sufficient research, that proves the fact wrong. This technique, when used in niches related to academia, can significantly increase the audience’s interest, and it will highlight your presentation as innovative.

Another approach is to debunk a myth using a fact. This contrast immediately piques interest because it promises to overturn commonly held beliefs, and people naturally find it compelling when their existing knowledge is put to the test. An example of this is when a nutritionist wishes to speak about how to lose weight via diet, and debunks the myth that all carbohydrates are “bad”.

10. The Power of Music

Think about a presentation that discusses the benefits of using alternative therapies to treat anxiety, reducing the need to rely on benzodiazepines. Rather than going technical and introducing facts, the presenter can play a soothing tune and invite the audience to follow an exercise that teaches how to practice breathing meditation . Perhaps, in less than 2 minutes, the presenter can accomplish the goal of exposing the advantages of this practice with a live case study fueled by the proper ambiance (due to the music played in the beginning).

11. Physical Activity

Let’s picture ourselves in an in-company presentation about workspace wellness. For this company, the sedentary lifestyle their employees engage in is a worrying factor, so they brought a personal trainer to coach the employees on a basic flexibility routine they can practice in 5 minutes after a couple of hours of desk time.

“Before we dive in, let’s all stand up for a moment.” This simple instruction breaks the ice and creates a moment of shared experience among the attendees. You could then lead them through a brief stretching routine, saying something like, “Let’s reach up high, and stretch out those muscles that get so tight sitting at our desks all day.” With this action, you’re not just talking about workplace wellness, you’re giving them a direct, personal experience of it.

This approach has several advantages. Firstly, it infuses energy into the room and increases the oxygen flow to the brain, potentially boosting the audience’s concentration and retention. Secondly, it sets a precedent that your presentation is not going to be a standard lecture, but rather an interactive experience. This can raise the level of anticipation for what’s to come, and make the presentation a topic for future conversation between coworkers.

12. Acknowledging a Person

How many times have you heard the phrase: “Before we begin, I’d like to dedicate a few words to …” . The speaker could be referring to a mentor figure, a prominent person in the local community, or a group of people who performed charity work or obtained a prize for their hard work and dedication. Whichever is the reason behind this, acknowledgment is a powerful force to use as a method of starting a presentation. It builds a connection with the audience, it speaks about your values and who you admire, and it can transmit what the conversation is going to be about based on who the acknowledged person is.

Closing Thoughts

Now you know how to start your presentation – you have the opening lines, you have the slides to use, and you can browse even more attractive PowerPoint presentation slides and templates on our website. Also, we recommend you visit our article on how to make a PowerPoint Presentation to get familiarized with the best tactics for professional presentation design and delivery, or if you need to save time preparing your presentation, we highly recommend you check our AI Presentation Maker to pair these concepts with cutting-edge slide design powered by AI.

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introducing group in presentation

  • November 2, 2023

Mastering Group Presentations: A Comprehensive Guide

  • Public Speaking

I n certain academic and business situations, delivering a group presentation can be more valuable than a solo one. Not only does it help alleviate the pressure on individuals, but it also promotes collaboration and the production of cohesive work. However, preparing for a group presentation requires careful organization and understanding of the audience . In this comprehensive guide, we will explore the key steps to master group presentations, from preparation to delivery, and provide practical tips for success.

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Preparing for the Group Presentation

Like any presentation, a group presentation requires significant preparation. The key to success lies in organizing the group effectively, considering multiple personalities and ensuring a cohesive final product.

Choosing a Presentation Moderator

To facilitate organization, the group should appoint a presentation moderator, essentially the “leader” of the group. The presentation moderator has the final say in decision-making and can allocate speakers for specific questions during the Q&A session.

Understanding the Audience

To make a presentation engaging, it is crucial to consider the audience and tailor the content to their needs. Assessing the audience’s prior knowledge and expectations of the topic helps determine the appropriate level of technicality and detail. For example, presenting the topic of bridge building to civil engineers allows for the use of technical language, while presenting to secondary school students requires simpler explanations.

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Defining the Presentation’s Purpose

Before diving into the content, the group must agree on the purpose of the presentation. Defining a clear message ensures that all subtopics contribute to the overall aim. For example, if the presentation aims to explore the effectiveness of different treatments for social anxiety, the group can build key points around this central theme.

Dividing the Presentation

A well-structured presentation should have a clear beginning, middle, and end. Divide the content into main sections, carefully considering the order of subtopics. The typical presentation structure includes:

  • Introduction: The first minute of the presentation should capture the audience’s interest and provide an overview of the presentation’s structure. Clearly state the aims and objectives, such as exploring the effectiveness of different treatments for social anxiety.
  • Middle Sections: These sections address the main points of the presentation, providing information that supports the overall aim. Depending on the topic, there can be one or more middle sections.
  • Conclusion : Summarize the key points and present a clear conclusion that ties everything together. Assign this section to the best speaker who can effectively synthesize the information presented.

Establishing a time sequence and setting deadlines for each task within the presentation ensures smooth progress and timely completion.

Sharing Responsibility

Unequal participation within a group can lead to disharmony and reduced cohesion in the presentation. Avoid this by assigning each speaker a specific section to work on based on their interests and expertise. Clear expectations and time management guidelines should be communicated to all group members.

Building the Presentation Together

To ensure a cohesive and seamless presentation, it is crucial to build it together as a group. This collaborative approach offers several benefits:

Avoiding Duplication of Content

By working together, the group can avoid duplicating content and ensure that each speaker’s section seamlessly connects with the others. This prevents confusion and maintains a coherent flow throughout the presentation.

Creating Consistency in Slides

While each speaker can work on their own slides, one individual should be responsible for merging them to ensure consistency in design and formatting. Collaboration enables feedback and edits to be made collectively, resulting in a polished final product.

Receiving Feedback

Meeting up to build the presentation allows for valuable feedback on speeches before presenting to an audience. The group can collectively review and refine each speaker’s content, ensuring clarity and relevance.

Establishing a Unified Conclusion

Building the presentation together enables the group to agree on the concluding section. This ensures that all key points are summarized effectively and the presentation concludes with a strong and cohesive ending.

Maintaining Balanced Speaking Time

By working together, the group can ensure that each speaker talks for a similar amount of time and covers a similar amount of information. This balance enhances the overall flow of the presentation and keeps the audience engaged .

Crafting a Compelling Opening

To captivate the audience from the start, consider opening the presentation with a relevant and engaging story. For example, when discussing the benefits of pets on physical and psychological health, share a story or study about someone whose quality of life significantly improved after getting a pet. Incorporating stories into presentations helps make them more memorable and relatable.

Knowing Each Speaker’s Content

To avoid repetition and promote seamless transitions, each speaker should be aware of what the other group members will say. This knowledge allows for cross-referencing between sections, enhancing the coherence and flow of the presentation. Additionally, if a team member is unable to attend, it becomes easier to find a replacement within the group.

Writing and Practicing Transitions

Smooth transitions between speakers contribute to a well-structured and engaging presentation. When transitioning, briefly recap the previous section, introduce the next speaker and their topic, and gesture towards them to signal the handover. Practice these transitions to ensure a seamless flow and keep the audience engaged throughout the presentation.

Rehearsing the Presentation

Rehearsing the presentation multiple times as a group is essential for success. This practice allows the group to evaluate the structure, timing, and content of the presentation. It also increases familiarity with the material, boosting confidence and improving responses to questions. Regular rehearsal sessions help the group identify any necessary edits and ensure a polished delivery.

Handling Nerves Before the Presentation

Nervousness before a presentation is natural, regardless of the audience size. Here are some tips to manage pre-presentation nerves:

Remind Yourself of the Audience’s Expectations

Remember that the audience is there to listen and wants you to succeed. They are likely to empathize with your nerves, as they may also have their own presentations to deliver. Recognizing this shared experience can help alleviate anxiety.

Practice and Familiarize Yourself with the Material

Practicing with your group and rehearsing your section at home builds familiarity and confidence. It allows you to become comfortable with the content and delivery, reducing anxiety.

Focus on Controlled Breathing

Nervousness can lead to rapid breathing, increasing anxiety levels. Practicing controlled breathing techniques can help regulate your breathing and reduce anxiety. Before the presentation, sit upright and take deep breaths in through your nose, filling your abdomen. Hold the breath for a few seconds, then exhale through your nose for a longer duration. Repeat this cycle to calm your nerves .

Avoid Filler Words

When nervous, people tend to use filler words like “um” and “uh” to fill gaps in their speech. Practice pausing instead of using filler words. Embrace the silence and speak deliberately, allowing your words to convey your message effectively.

During the Group Presentation

Once the presentation begins, there are several key considerations to ensure a confident and engaging delivery.

Introduce the Team

The presentation should start with the presentation moderator introducing the team, rather than each individual introducing themselves. This approach creates a smoother transition into the content and enhances the overall cohesion of the presentation.

Pay Attention to the Presentation

While waiting for your turn to speak, actively listen to your colleagues’ presentations. Display interest and engagement in their content, even if you have heard it before. This non-verbal support contributes to a positive group dynamic and keeps the audience engaged.

Utilize Body Language and Eye Contact

Body language is a powerful tool for engaging the audience. When it’s your turn to speak, stand slightly in the foreground of the group, smile at the audience, and make eye contact. Keep your arms uncrossed and avoid looking down at your notes or slides. Instead, face the audience and maintain eye contact as you speak.

Vocal Variety

How you deliver your speech is just as important as the content itself. Adapt your voice to emphasize important points, raise or lower your voice for intensity, and avoid speaking in a monotone manner. Sound enthusiastic and confident, as your tone can significantly impact audience engagement. Speak loudly and clearly, ensuring that everyone can hear you. If you notice yourself speaking too quickly, pause and slow down to maintain clarity.

Warm Up Your Voice

Before starting the presentation, warm up your voice by taking short pauses and breathing deeply. This exercise helps you achieve vocal variety and ensures that your voice remains clear and strong throughout the presentation.

Managing Nervous Behaviors

It’s natural to feel nervous during a presentation, but it’s important to manage nervous behaviors. Avoid shifting your weight or fidgeting, as these actions can distract the audience. Remember that the audience is unlikely to perceive your anxiety as strongly as you feel it.

Delivering a Strong Conclusion

The conclusion is a critical part of the presentation, as it is the last section the audience will remember. Summarize the key points and lead into a clear concluding statement that reinforces the main message. For example, when discussing the impact of social media on self-esteem, list the main points covered and conclude with a definitive statement based on the evidence presented.

Handling Questions and Answer Sessions

The Q&A session after the main presentation can be challenging, as the questions asked may be unpredictable. However, working as a group allows for a distributed knowledge base and ensures that each question is addressed by the most knowledgeable speaker. When answering questions:

  • Pause before responding to gather your thoughts.
  • Focus on directly answering the question without providing unnecessary information.
  • If you don’t understand a question, ask for clarification to avoid providing irrelevant answers.
  • It’s okay not to have all the answers. If you’re unsure, acknowledge it and offer to follow up with additional research.

Ending the Presentation

A strong ending is crucial to leave a lasting impression. The presentation moderator should thank the audience and, if applicable, smoothly transition to the next group or topic. This final gesture provides closure and ensures a professional conclusion to the presentation.

Mastering group presentations requires effective organization, collaboration, and preparation. By following the steps outlined in this comprehensive guide, you can confidently navigate the process from start to finish. Remember to choose a presentation moderator, understand your audience , divide the presentation into sections, share responsibilities, build the presentation together, utilize stories to engage the audience , practice transitions, manage nerves, and deliver a strong conclusion. With practice and a collaborative mindset, you can excel in group presentations and effectively communicate your message to diverse audiences . So, embrace the opportunity to work as a team, learn from one another, and grow your public speaking skills through group presentations .

Build Career Skills Online: Fast-track your career with award-winning public speaking classes and courses. Boost your presentation skills with executive coaching and business coaching. Contact us today .

Key Takeaways

I. Introduction A. Importance of group presentations in academic and business contexts B. Benefits of group presentations, including pressure alleviation, collaboration, and cohesive work C. Overview of the comprehensive guide

II. Preparing for the Group Presentation A. Choosing a Presentation Moderator B. Understanding the Audience C. Defining the Presentation’s Purpose D. Dividing the Presentation E. Sharing Responsibility F. Building the Presentation Together G. Crafting a Compelling Opening H. Knowing Each Speaker’s Content I. Writing and Practicing Transitions J. Rehearsing the Presentation K. Handling Nerves Before the Presentation

III. During the Group Presentation A. Introduce the Team B. Pay Attention to the Presentation C. Utilize Body Language and Eye Contact D. Vocal Variety and Warm-Up Exercises E. Managing Nervous Behaviors F. Delivering a Strong Conclusion G. Handling Questions and Answer Sessions H. Ending the Presentation

IV. Conclusion A. Recap of key points in mastering group presentations B. Encouragement to embrace teamwork and collaborative learning C. Call to action: Build career skills online with public speaking classes and executive coaching

V. Call to Action A. Invitation to start a free trial for online public speaking classes and courses B. Information on how to access executive coaching and business coaching services

This comprehensive guide provides a step-by-step approach to mastering group presentations, emphasizing the importance of organization, collaboration, and preparation. By following the outlined strategies, individuals can confidently deliver engaging and impactful presentations, enhancing their public speaking skills and professional development.

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How to Deliver Group Presentations: The Unified Team Approach

When you’re asked to present as part of a panel of experts or a team making a sales pitch, you might think that there is safety in numbers and that you need to prepare less than if you were speaking on your own.

The truth is that, for your audience, a group presentation is only as strong as its weakest presenter. Here’s how to help your team create a strong and unified group presentation .

3 Ingredients of Great Group Presentations

The three ingredients to develop and deliver a unified group presentation are clarity, control, and commitment.

Clarity of Purpose

Clarity of roles, clarity of message, control introductions, control transitions, control time and space, commit to a schedule, commit to rehearsing.

  • Commit to Answering Your Audience’s Questions

Incorporating these elements will give your audience a “seamless” message.

Ingredient #1: Clarity

Just as your presentation will have a clear purpose, expressed in a thesis statement, your group should create a Charter Statement that explicitly captures the group’s desired outcome.

The charter is different from a thesis statement. The thesis specifically frames the presentation message whereas the charter frames your group’s purpose. This Charter Statement becomes the test of everything that will go into the presentation and help guide the efforts of the team. The charter and the thesis may overlap, but even your thesis statement must be tested against the group’s Charter.

For example, if your group agrees that your general purpose is to sell your product, and, more specifically, you know that the key decision maker in the audience is leery about cutting checks to companies like yours, build that into your Charter Statement.

The purpose of our presentation is to sell our Product to ABC Company by overcoming the objections of the company’s Purchasing Officer through clear examples of how our Product provides a fast return on investment.

The Charter Statement will come in handy when you have a team member who may want to go “off track” to tell personal anecdotes that don’t pass the test of the group’s charter.

Personalities come into play when groups meet to develop presentations. Jockeying for position and ego struggles can quickly deplete the group’s momentum, resulting in hurt feelings and, potentially, a weaker presentation. Providing clarity to group roles helps to establish expectations and keep the entire group moving towards a common objective: a great group presentation.

“ Developing clarity within your group will help you develop a clear message for your audience. ”

Identify the roles your group needs during message development. For example, to ensure that team members are meeting assignments, select a Project Manager . This person isn’t the “boss of the presentation”, but rather will focus on schedule and assignments.

Other roles could include a Gap Analyst who is responsible for identifying “gaps” in content and support materials (handouts, graphics, etc.), which in turn could work closely with other roles within the group like the Chief Researcher .

Capitalize on the unique personalities within your group to develop roles that work well for all, but be sure to discuss the roles openly so they are clear to everyone.

Instead of writing “speeches” for each individual speaker , try creating one master presentation , a unified narrative, and then decide who speaks to which points, and when.

This is a shift from the traditional segmented method of group presentations where often group members are directed to “give five minutes of talking” and then are left to develop content independently.

In a master presentation, each speaker may weave in and out at various points during the presentation. When done well, this fluid dynamic can hold an audience’s attention better by offering a regular change in speakers’ voices and presence.

By using a master presentation, your group will ensure that each of the presenters will stay “on script” and use cohesive language, smooth transitions, and (when using visuals) consistent graphics.

Ingredient #2: Control

Your audience notices how your group introduces itself, so plan those introductions with your presentation.

Your presentation may be part of a larger event that includes an emcee who will introduce the team. If so, be sure that you provide pertinent information to the emcee that will allow her/him to generate interest in your presentation even before you begin speaking.

If your group is responsible for making its own introductions, however, you will need to decide if you will introduce your group members in the beginning, or when they first speak. Your group also will need to decide if each member introduces her/himself, or if one member will introduce everyone.

There is no one right way to do introductions, but your group must decide how to do them before the day of the presentation.

Decide how you are going to “hand off” from one speaker to the next. In the “master presentation” approach, you may want to consider simply have speakers pick up a narrative right where the previous speaker left off.

“ Your audience notices how your group introduces itself, so plan those introductions with your presentation. ”

If you use the more traditional segmented approach, each speaker may cue the subsequent speakers by identifying them and their subject matter. For example:

“…and speaking of quality control, no one is more qualified the Bob Johnson. Bob is going to tell us about how this team will deliver a quality project for you.”

Another option is to assign a group emcee who will handle transitions between presentation sections. Your group will need to determine which option makes the most sense based on your presentation style and audience expectations.

Multiple speakers translate to occupying more physical space, and the potential to gobble up more time with introductions and transitions.

If you will be presenting in a small room, consider where each speaker needs to be positioned to quickly reach the speaking area, and whether they will sit or stand when not speaking.

Your presentation must fit within your allotted time, so you will need to time your group’s presentation, including equipment set up, introductions, and transitions.

Ingredient #3: Commitment

Once you know the date of your presentation, create a schedule that includes specific milestones, such as “presentation draft due” and “final rehearsal”. Having a specific schedule allows members either to agree to the group’s expectations or to offer dates that better fit their personal schedules.

Additionally, you can assign specific responsibilities to the scheduled milestones; for example, who is responsible for bringing the handouts, projector, and laptop to the presentation?

“ If you find group members who lack the commitment to rehearse, consider finding group members who will commit. ”

Rehearsing is one of the most important steps for presentation success. Have your team members agree from day one that they will make themselves available to practice with the group.

If you find group members who lack the commitment to rehearse, consider finding group members who will commit. Practice makes perfect, and no rehearsal means your group doesn’t know what will happen to the content, timing, or quality of the presentation. Do those sound like things your group would like to leave to chance?

Commit to Answering Your Audience’s Questions

Once your formal presentation is over, you may see some raised hands in the audience, ready to pepper your group with questions. Your presentation is not over yet. How you handle those questions is as important as the presentation itself. A well-done presentation means nothing if presenters fumble questions so badly that they appear incompetent.

Have each member develop a list of potential questions and then, as a group, review the list. Discuss who will be responsible for handling which types of questions. Are there any questions important enough to build into the presentation?

From a Rag-Tag Group of Speakers to a Dynamic Presenting Team

By incorporating these three ingredients into your next group presentation process, you will find that you not only develop a presentation that your audience loves, but your group will transform from a rag-tag group of speakers into a dynamic presenting team.

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Great article — what I have found over the years with group presentations (2 or more people) is that the transitions are critical for success. Done well, with good chemistry, and a group presentation is fun to watch. Done badly, with awkward moments, and a group presentation becomes a group debacle.

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How to Deliver Group Presentations: The Unified Team Approach http://bit.ly/3xVq3Z II nice read — Harish Nair Nov 4th, 2009
How to Deliver Group Presentations: The Unified Team Approach via @6minutes #eventprofs http://ow.ly/EHEP — Jeff Hurt Nov 23rd, 2009
Just did a group pitch — NOT easy RT @JeffHurt: How to Deliver Group Presentations via @6minutes #eventprofs http://ow.ly/EHEP — LucyHackman Nov 23rd, 2009
推荐了文章:How to Deliver Group Presentations: The Unified Team Approach( http://XianGuo.com/item/758830453 )。 — AT Chen Nov 29th, 2009
@robert_g_turner You may enjoy my article on group presentations. http://t.co/F5DwBbkD — Chaunce Stanton May 8th, 2012
My students are starting their Team Teaching Presentations this week. I think I'll share this with them: http://t.co/KLu0mAOX #techcomm — Nicholas Carrigg Oct 1st, 2012
#furlongspeechclass READ THIS! How to Deliver Group Presentations: The Unified Team Approach http://t.co/kXGGwFk9Eq via @6minutes — @speechteach912 Apr 22nd, 2014
@Chaunce_Stanton Hi Stanton, I have just read your article on group presentation. I found it really helpful for me. http://t.co/nVClZrr5ok — @iamdpnkr Sep 30th, 2014
How to Deliver Group Presentations: The Unified Team Approach http://t.co/61Qwr9EuuK via @6minutes — @tgillihan Aug 19th, 2015
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How to Introduce Yourself in a Presentation: Guide to a Killer Opener

Hrideep barot.

  • Body Language & Delivery , Speech Writing

how to introduce yourself in a presentation

Not sure how to introduce yourself in a presentation? Hang on till the end of this article.

Giving a presentation can be unnerving. And introducing yourself can be nerve-wracking.

But, without a fitting introduction, you would just be hitting the dart in a dark room.

The usual “Good Morning! I’m Neil, and I work as a Designer at…” is boring and doesn’t cut the ice anymore.

So, how to Introduce yourself in a presentation or start with a killer opener?

Introducing yourself in a presentation is pitching yourself to the audience so they stick around for the rest of your talk. Include your background, your unique trait, and who you are while sticking to the context in the first 30-60 seconds of your introduction.

Your introduction should be effective and have an interesting hook. You’ve got to nail your introduction in one shot.

A make or break moment indeed.

But, fret not! We’ve outlined what to say before starting a presentation to help get your next presentation right.

Occasions Where you Might Have to Introduce Yourself in a Presentation

Here is what to say to start a presentation on some of the occasions where you would have to introduce yourself before the presentation.

Though the principle focus will be about yourself, tweaking your intro to the context and the place is essential.

The self-introduction should be compelling enough to woo your audience to sit for the next couple of minutes.

1.How to Introduce Yourself in a Business Environment

Introducing yourself in your workplace can be rather common. But, it’s during business meetings and conferences where you need to stand out.

Every time you meet senior managers, introducing yourself with your name and job title doesn’t grab eyeballs anymore.

However, taking the first step matters. Here are certain scenarios where you might be called upon to introduce yourself in your workplace.

How to Introduce Yourself in an Interview Presentation

The “Tell me about yourself” in interviews is intimidating. If you’ve found alibi’s to every presentation in your school and college, it doesn’t work here anymore.

Prepare a short introduction about yourself and be interview-ready. Anytime someone hits you up with that question, you need to be able to answer it with the snap of a finger.

Here is an example of a self-intro during an interview.

“As a skilled designer, with two years of freelance experience, I’ve worked for clients with diverse needs. I’ve also designed brochures, magazines, logo , and packaging materials for my friend’s company. I’m confident that I can leverage my skills and bring in the best for your brand.

How to Introduce Yourself and Your Team in a presentation

Business meetings can be boring. But there are times where you might have to introduce yourself to a new co-worker or a senior leader.

As a team leader yourself, you might have to introduce yourself and your team to present on the performance of the company the previous month.

Presentation introduction ideas if you’re a marketing executive can be,

An increased conversion of 130%, that’s what our marketing team achieved last quarter making our campaign a massive success. The soldiers who made this possible are Ryan, who made sure the User Experience on our website was flawless. Sean who ensured seamless technical functioning, and Abby who is responsible for all the copies on our major assets. I’m John, who heads the marketing team and we want to take you through all the activities we actioned, the metrics we achieved, and the lessons we learned from our recent efforts.

In case you are giving a group presentation , you can check out this video to see how you can introduce different members of your group for seamless transitioning:

How to Introduce Yourself in a Conference Presentation

In a conference presentation, you’re expected to be a little formal. While you can adhere to that school of thought, don’t forget to story tell. That’s what hooks an audience! Here is an example of how to introduce yourself in a business conference:

“Today, I’m going to share a story of how someone with zero marketing skills and training made it to the top by creating massive revenue streams through online campaigns and paid advertising in just 6 months. If you’re passionate about digital marketing, this is for you. Stay tuned till the end for better insights.

If you’re presenting at a business conference, take a look at these 11 tips for presenting at a conference by Brian Campbell.

How to Introduce Yourself in a Business Pitch Presentation

Now, this is for entrepreneurs who are starting out. If you need investors to fund your start-up, you need to have a solid pitch.

 Let’s say, your product is AI-driven that alerts drivers who doze off while driving.

Talk about the benefits of it in a single sentence and highlight the downsides of dozing off while driving with stats and figures.

Check out this Crucial Public Speaking Tips for Startup Founders written by us that’ll help you nail your pitch.

Also, have a look at this video below. In this, Josh Light introduces himself in just two simple sentences and moves on to talk about his start-up. It is simple yet effective.

How to Introduce Yourself in Client Presentation

If you’re a freelancer, talking to clients can be a daunting task.

Let’s say you’re an engineer turned copywriter. That’s an interesting combo out there, and if you put it out in a way you write your copy, it would benefit you to a whole another level.

“I’m an experienced travel copywriter and I’ve written ad copies, sales pages, newsletters, landing pages for some of the top travel brands. I have over 5 years of expertise in this niche. One of my landing page copy at XYZ converted 50% of eyeballs into leads thus scaling up revenue drastically and I’m here to do the same if you see me fit after this call.”

2 . How to Introduce Yourself in a Presentation as a Student

how to introduce yourself in a presentation

Are you that kid/student who always shied away from giving presentations? Did you always come up with excuses and ended up giving barely one or two presentations your whole school life?

Yes? Well, it’s time to come out of your cocoon as it won’t work out that way in college or at work.

Whether it’s a small project presentation or giving a speech in your English class, here is how you can introduce yourself as a student.

How to Introduce Yourself in a Seminar Presentation

We’ve all been there. Hundreds of projects and assignments, be it school or college.

And that’s where you have to introduce yourself before jumping into your project. No matter how good your project, a solid introduction can put you ahead of the game.

“ As a tech enthusiast myself, I was intrigued by blockchain technology for a long time and today I have my project built using that very technology. I’m so excited to share with you all the working of this model and its benefits. Let’s jump right in.

It’s pretty easy and to-the-point. You need to be self-confident while saying those two lines and try to avoid fillers.

3. How to Introduce Yourself as a Trainer

As a trainer or teacher, your audience may be high-school students, undergrads, or even professionals.

Depending on the setting and the audience, you can craft your intro effectively and be of interest to the listeners.

How to Introduce Yourself to Students

As a teacher in a new school or college, introducing yourself is obligatory.

You can go about it this way if you’re a Moral Science teacher or Counselor:

“Hi everyone! I’m Alexandra. Call me Alex for short. We are going to have loads of fun for the next couple of months as I will be handling your Moral Science classes from today. If you are stuck in a dilemma or facing challenges, you can talk to me personally anytime and I’ll help you find a way out.

How to Introduce Yourself in a Workshop

Workshops are where you learn about a subject.  What if you’re the one who is conducting the workshop or needs to fill in for your friend for a couple of minutes, you need to introduce yourself.

 If you’re an Economics Graduate who is conducting a Calligraphy workshop, your presentation starting words can be something like,

  “Back when I was a kid, I used to scribble down letters I saw on posters and fell in love with the notion of lettering and calligraphy. I wanted to get into design, but I thought it was a fleeting moment and took Economics. Little did I know how much it meant to me. I finally figured what to do in life, and here I’m helping and teaching you to do what you love after years of learning and unlearning.”

How to Introduce Yourself in Training Sessions

Whether you’re a corporate trainer or getting into training students after years of experience, introducing yourself never gets old.

You can emphasize your past experiences in the form of a story or start with how it was when you worked with one of the top clients in the industry.

Below is an example to give you a precise picture.

“How excited are you to get your first gig? I’ve been a freelance writer for over a decade now. And freelancing is one of the best jobs as it gives you financial freedom and lets you work from the comforts of your couch or at your favorite café. So, I’m here to teach you to do the exact same thing and help you find your passion.”

5 . How to Introduce Yourself in a Video Presentation

how to introduce yourself

Virtual presentations are a thing right now. If you’re a camera conscious person, you might have a hard time giving a presentation.

Dressing well and looking at the camera and not the screen can help present better. And always, look into the camera and not the screen when it comes to virtual presentations.

No matter how tensed you are, do not reflect it on your face. Have a bottle of water beside you to buy time and calm your nerves.

Here are two possible situations where you might have to introduce yourself virtually. 

How to Introduce Yourself in Webinars

Webinars are ever-increasing and if your introduction is not crisp and strong enough, building an online presence can be challenging.

Here is how you can introduce yourself in a webinar:

“ Hi, guys and welcome to this long-awaited session. How excited are you all? I know I am! We’re live and will be having John in a while. I’m so thrilled to see hundreds of you all attending this webinar live. It’s going to be a great session. I’m Patrick and the head of Marketing at XYZ. We started this webinar series two months ago and received phenomenal feedback from you all. And that’s why we’re back again with another one. Thank you and welcome again! Hope you find this session valuable.”

How to Introduce Yourself in a Virtual Presentation

Now, this is for freshers whose onboarding is going virtual. Whether it’s training sessions, virtual presentations, or virtual meetings, you are asked to introduce yourself to every manager and executive multiple times in a day.

Hey everyone! I’ve always loved meeting new people and though this is virtual now, just so thrilled to see you all on screen. If you see a new face popping on your screen during meetings and conferences, that’s me, John the new joinee. Can’t wait to meet you all in-person. Excited to jump-start my career here.

You can also check out this video we made to know certain ninja hacks to engage a virtual audience:

Related Article: All You Need To Know About Presenting Remotely

How to Structure an Intro – How to Start and End

  • Add a Compelling Hook

You can begin your speech with a fact or a question to pique curiosity of your audience.

  • A Brief Overview about Yourself

In those initial few seconds, greet the audience and talk about your strength or any unique trait in a word or two.

You can mention your achievements or contributions before talking about your background.

  • A Quick history or Timeline of your Career/Education

In any context, a brief background or history about yourself should be talked about to let your audience know a little more about you.

It helps them gain trust and reliability.

  • Smooth transition to the main topic

You shouldn’t abruptly move to the heart of your speech post introduction. There should be a subtle transition to make it effective.

Here is a presentation introduction example,

“Would you believe if I told you that you could reach 15k+ people on LinkedIn in just 30 days? No? Stick around for the next 7 minutes as I’m going to teach you all about it so you can get started as a rookie with zero connections.” Hi everyone! I’m XYZ – a Linked Growth Hacker. I’ve been helping businesses grow and build a strong personal brand for five years now. If you’re wondering how to generate leads on LinkedIn, take note of the pointers I’ll be sharing with you today.”

Magic ingredients to Introduce Yourself in a Presentation

introducing group in presentation

You’ve got to nail your introduction no matter where you give the presentation.

You need to learn the art of introducing yourself because that’s the one thing you’ll be asked everywhere when you meet new people.

Introducing yourself is like marketing yourself. A stellar introduction can make a difference.

Here are some surefire ways to stand out in a crowd with your introduction.

With practice, your self-introduction will improve over time if you follow these tips. 

1 . Brevity is Key

We all know this by now. No matter how many years of experience you have or how much you’ve contributed to the team, your introduction should be short yet powerful.

With an impressive introduction about yourself, your audience will be keen on listening to you more. 

2 . Talk about Your Contribution

Instead of starting with your name and your job title, craft a story about the time you have to strive hard to achieve a goal be it personal or professional.

Speak about your contribution subtly without coming off as someone narcissistic. Unfold the little moments and share them with the audience.

Ensure it is related to your speech. Don’t go off course.  

3 . Understand Where You Are

The place where you present matters though it is about you. You need to research about the people, the place and craft an introduction aligning with it.

Keep it relatable. Get the audience to be on track with you. Keep your message clear and introduce it in a way it is memorable. 

4. Be as Real as Possible

Since you are introducing yourself, be as real as possible.

No, you don’t have to be extremely personal, but you can keep it minimal and include a common ground so that the audience can resonate with you.

5. A Smooth Transition is Essential

Transitioning from your intro to the main speech needs to be done right to keep the flow going.

Craft an intro and shift to the main topic without a pause after the introduction.

6. Create a Hook

Creating a hook is essential no matter the setting you’re introducing yourself in.

You need to grab the attention of the audience with your first sentence. You can quickly introduce yourself in a few sentences without taking much time.

Begin with a question or an interesting fact to hook the listeners every time you introduce yourself.

Want some inspiration? Here is a very practical video we have made on different opening lines from some of the most powerful speeches. Hopefully, it will get your creative juices flowing for what your hook should be:

Level up your public speaking in 15 minutes!

Get the exclusive Masterclass video delivered to your inbox to see immediate speaking results.

The Masterclass video is on its way to your inbox.

Concluding Thoughts

Introducing yourself in a presentation can be stressful. You won’t get it right on your first. Nope. Not on your third attempt.

Heck! Not even on your sixth introduction too.

But, here’s the thing.

You need to keep sailing and believe in yourself. That’s what can make you better.

If you want to evolve as an individual, learning how to introduce yourself can immensely contribute to your professional and personal growth.

Push your boundaries and cross your personal threshold. You will get there one day. And introducing yourself will no longer be a daunting task.

Hrideep Barot

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How to Introduce Yourself in a Presentation [with Examples]

How to Introduce Yourself in a Presentation with Examples

In this post, we are going to cover the best way, a very simple three-step process that will help you introduce yourself in a presentation. A summary of the steps is below.

  • Start with your name and company (or organization or school).
  • Tell your audience what problem you can solve for them.
  • Share some type of proof (social proof works best) that you can solve this problem.

I will break down each step into a simple-to-follow process. But first… a little background.

First, Identify What Your Audience Wants from Your Presentation

Create an Introduction for Yourself that Makes the Audience Care About the Topic

So, before you design your introduction, think about what your audience wants from your presentation. Why do they want to spend their valuable time listening to you? Are going to waste their time? Or, are you going to provide them with something valuable?

For instance, I have expertise in a number of different areas. I’m a public speaking coach, a keynote speaker, a best-selling author, a search engine optimization specialist, and a popular podcaster. However, if I delivered that sentence to any audience, the most likely reaction would be, “So what?” That sentence doesn’t answer any of the above questions. The statement is also really “me-focused” not “audience-focused.”

So, when I start to design my self-introduction, I want to focus just on the area of expertise related to my topic. I’m then going to answer the questions above about that particular topic. Once you have these answers, set them aside for a second. They will be important later.

How to Introduce Yourself in a Presentation in Class.

If Everyone Already Knows You DON'T Introduce Yourself

Instead, you probably want to add in a fun way to start a speech . For example, instead of introducing yourself in your class speech and starting in an awkward way, start with a startling statistic. Or start with a summary of your conclusion. Or, you could start the presentation with an inspirational quote.

Each of these presentation starters will help you lower your nervousness and decrease your awkwardness.

If you are delivering a speech in a speech competition or to an audience who doesn’t know you try this technique. Just introduce yourself by saying your name , the school you represent , and your topic . Make it easy. This way you get to your content more quickly and lower your nervousness.

Typically, after you get the first few sentences out of the way, your nervousness will drop dramatically. Since your name, school, and topic should be very easy to remember, this takes the pressure off you during the most nervous moments.

Obviously, follow the guidelines that your teacher or coach gives you. (The competition may have specific ways they want you to introduce yourself.)

How to Introduce Yourself in a Business Presentation — A Step-by-Step Guide.

How to Introduce Yourself in a Business Presentation-A Step-by-Step Guide

In a professional setting, when new people walk into a meeting and don’t know what to expect, they will feel uncomfortable. The easiest way to ease some of that tension is to chat with your audience as they come into the room.

By the way, if you are looking for a template for an Elevator Speech , make sure to click this link.

Step #1: Start with your name and company name (or organization).

This one is easy. Just tell your audience your name and the organization that you are representing. If your organization is not a well-known brand name, you might add a short clarifying description. For instance, most people outside of the training industry have never heard of The Leader’s Institute ®. So, my step #1 might sound something like…

Hi, I’m Doug Staneart with The Leader’s Institute ®, an international leadership development company…

Still short and sweet, but a little more clear to someone who has never heard of my company.

Should you give your job title? Well… Maybe and sometimes. Add your title into the introduction only if your title adds to your credibility.

For example, if you are delivering a financial presentation and you are the Chief Financial Officer (CFO) of your company, you might mention that. Your title adds to your credibility. However, if the CFO is delivering a presentation about the value of joining a trade association, the CFO title adds little credibility. So, there is very little value in adding the title.

Step #2: Tell your audience what problem you can solve for them.

Identify the Problem You Solve for Your Audience

For instance, if my topic is how to deliver presentations, I have to determine why the audience would care. What problem will they have that I can help them with? For my audiences, the problem that I most often help people with is how to eliminate public speaking fear. Once I have the problem, I add that to my introduction by using the words, “I help people…”

Hi, I’m Doug Staneart with The Leader’s Institute ®, an international leadership development company, and I help people eliminate public speaking fear.

However, if my topic is How to Close a Higher Percentage of Sales Presentations , I’d likely want to alter my introduction a little. I might say something like…

Hi, I’m Doug Staneart with The Leader’s Institute ®, an international leadership development company, and I help people design more persuasive sales presentations.

I have expertise in both areas. However, I focus my introduction on just the expertise that is applicable to this audience. If I gave the first introduction to the second audience, they will likely respond by thinking, well, I don’t really get nervous speaking, so I guess I can tune out of this speech .

So, create a problem statement starting with, “I help people…” Make the statement apply to what your audience really wants.

Step #3: Share some type of proof (social proof works best) that you can solve this problem.

By the way, if you just do steps #1 and #2, your introduction will be better than most that you will hear. However, if you add Step #3, you will gain more respect (and attention) from your audience. Without adding some type of proof that you can solve this problem, you are just giving your opinion that you are an expert. However, if you can prove it, you are also proving that you are an expert.

This is the tricky part. For some reason, most people who get to this part feel like they haven’t accomplished great things, so they diminish the great accomplishments that they do have.

For instance, an easy way to offer proof is with a personal story of how you have solved that problem in the past.

A Few Examples of How to Introduce Yourself Before a Presentation.

For instance, one of my early clients was a young accountant. When I was working with him, he came up with the following introduction, “I’m Gary Gorman with Gorman and Associates CPA’s, and I help small businesses avoid IRS audits.” It was a great, audience-focused attention-getter. (No one wants to get audited.) However, as an accountant, it wasn’t like his company was getting a lot of five-star reviews on Yelp! So, he was kind of struggling with his social proof. So, I asked him a series of questions.

Me, “How many clients do you have?”

Gary, “Over 300.”

Me, “How many small business tax returns have you processed?”

Gary, “Well, at least a couple hundred a year for 15 years.”

Me, “So, at least 3000?” He nodded. “How many of your 300 clients have been audited since you have been representing them?”

He looked at me and said, “Well, none.”

So, we just added that piece of proof to his talk of introduction.

I’m Gary Gorman with Gorman and Associates CPA’s, and I help small businesses avoid IRS audits. In fact, in my career, I’ve helped clients complete over 3000 tax returns, and not a single one has ever been audited.

Here Is How I Adjust My Introduction Based on What I Want the Audience to Do.

For my proof, I have a number of options. Just like Gary, I have had a lot of clients who have had great successes. In addition, I have published two best-selling books about public speaking. I also have hundreds of thousands of people who listen to my podcast each week. So, I can pick my evidence based on what I want my audience to do.

For instance, if I’m speaking at a convention, and I want the audience to come by my booth to purchase my books, my introduction might sound like this.

Hi, I’m Doug Staneart with The Leader’s Institute ®, an international leadership development company, and I help people eliminate public speaking fear. One of the things that I’m most know for is being the author of two best-selling books, Fearless Presentations and Mastering Presentations.

However, if I’m leading a webinar, I may want the audience to purchase a seat in one of my classes. In that case, my introduction might sound like this.

Hi, I’m Doug Staneart with The Leader’s Institute ®, an international leadership development company, and I help people eliminate public speaking fear. For instance, for the last 20 years, I’ve taught public speaking classes to over 20,000 people, and I haven’t had a single person fail to reduce their nervousness significantly in just two days.

If my goal is to get the audience to subscribe to my podcast, my intro might sound like…

Hi, I’m Doug Staneart with The Leader’s Institute ®, an international leadership development company, and I help people eliminate public speaking fear. One of the ways that I do this is with my weekly podcast called, Fearless Presentations, which has over one million downloads, so far.

Use the Form Below to Organize How to Introduce Yourself in a Presentation.

The point is that you want to design your introduction in a way that makes people pause and think, “Really? That sounds pretty good.” You want to avoid introductions that make your audience think, “So what?”

If you have a speech coming up and need a good introduction, complete the form below. We will send you your answers via email!

Can You Replace Your Introduction with a PowerPoint Slide?

Is it okay to make your first slide (or second slide) in your presentation slides an introduction? Sure. A good public speaker will often add an introduction slide with a biography, portrait, and maybe even contact information. I sometimes do this myself.

However, I NEVER read the slide to my audience. I often just have it showing while I deliver the short introduction using the guide above. This is a great way to share more of your work experience without sounding like you are bragging.

For tips about how many powerpoint slides to use in a presentation , click here.

Remember that There Is a Big Difference Between Your Introduction in a Presentation and Your Presentation Starter.

When you introduce yourself in a presentation, you will often just use a single sentence to tell the audience who you are. You only use this intro if the audience doesn’t know who you are. Your presentation starter, though, is quite different. Your presentation starter should be a brief introduction with relevant details about what you will cover in your presentation.

For details, see Great Ways to Start a Presentation . In that post, we show ways to get the attention of the audience. We also give examples of how to use an interesting hook, personal stories, and how to use humor to start a presentation.

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Organizing Your Social Sciences Research Assignments

  • Annotated Bibliography
  • Analyzing a Scholarly Journal Article
  • Group Presentations
  • Dealing with Nervousness
  • Using Visual Aids
  • Grading Someone Else's Paper
  • Types of Structured Group Activities
  • Group Project Survival Skills
  • Leading a Class Discussion
  • Multiple Book Review Essay
  • Reviewing Collected Works
  • Writing a Case Analysis Paper
  • Writing a Case Study
  • About Informed Consent
  • Writing Field Notes
  • Writing a Policy Memo
  • Writing a Reflective Paper
  • Writing a Research Proposal
  • Generative AI and Writing
  • Acknowledgments

Planning for and Giving a Group Presentation

Students working on group projects are often asked to give an oral presentation summarizing the results of their research. Professors assign group presentations because they combine the cooperative learning benefits of working in groups with the active learning benefits of speaking in front of an audience. However, similar to participating in a group project , giving a group presentation requires making decisions together , negotiating shared responsibilities, and collaborating on developing a set of solutions to a research problem . Below are issues to consider when planning and while giving a group presentation.

Before the Presentation

When to Begin

Planning the logistics around giving a presentation should take place as the group project progresses and, most critically, coalesce immediately after results of your study are known and clear recommendations can be made. Keep in mind that completing the basic tasks of giving a presentation [e.g., designating a moderator, designing the slide templates, working on the introduction, etc.] can save you time and allow your group to focus just before giving the presentation on how to effectively highlight the most important aspects of the research study.

Sharing the Responsibility

Everyone in the group should have an equal role in preparing the presentation and covering a similar amount of information during the presentation. However, a moderator should be elected to lead the presentation. The group should then determine what each member will speak about. This can be based on either the member's interests or what they worked on during the group project. This means that each member should be responsible for developing an outline of what they will talk about and drafting the content of their section of the slides or other forms of visual aids.

NOTE: If , for whatever reason, a group member is  particularly anxious about speaking in front of an audience or perhaps they are uncomfortable because English is not their first language, consider giving them a role that can be easily articulated, such as, introducing the purpose of the study and its importance. Everyone must participate in speaking, but be cognizant of the need to support that person by discussing what would work best for them while still being an active contributor to the presentation.

Organizing the Content

The content of the presentation should parallel the organization of the research study. In general, it should include a brief introduction, a description of the study, along with its purpose and significance, a review of prior research and its relevance to your group's project, an analysis of the results, with an emphasis on significance findings or recommended courses of action, and a brief statement about any limitations and how the group managed them. The conclusion of the presentation should briefly summarize the study's key findings and implications and, if time has been allotted, ask for questions from the audience. The conclusion can also be used to highlight areas of study the require further investigation. Note that the group's time should be spent primarily discussing the results of the study and their implications in furthering knowledge about the research problem .

Developing the Content

The narrative around each section must flow together smoothly t o ensure that the audience remains engaged. An initial meeting to discuss each section of the presentation should include the following: 1) deciding on the sequence of speakers and which group member presents on which section; 2) determining who will oversee the use of any technology [and who steps up when it's that person's turn to speak]; 3) determining how much time should be allocated for each section in relation to the overall time limit; 4) discussing the use and content of slides or other visual aids; and, 5) developing a general outline of the presentation. Once everyone's roles and responsibilities have been negotiated, the group should establish a schedule of deadlines for when the work should to be completed.

Creating Transitions

Building the narrative of an oral presentation means more than imparting information; it also requires the group to work together developing moments of transition from one section to the next. Transitional statements ensures coordination among members about what is to be covered and helps your audience follow along and remain engaged. The transition from one section to the next should include both verbal cues [e.g., a recap what you just discussed and an introduction of the next speaker] and non-verbal gestures [e.g., stepping away from the podium or front of class to make room for the next speaker]. An example of this transition could be something like this:

Speaker 1: " ...so to summarize, the literature suggested that allegations of election fraud often created the conditions for massive street protests in democratized societies. Next Mike will discuss how we analyzed recent events in Mexico and determined why this assumption may not apply under certain conditions. "

Speaker 2: " Thank you, Jordan. Next slide. In our study, we coded and analyzed the content of twitter accounts to explore the rise of dissension among.... "

NOTE:   Each member of the group should learn the entire presentation and not just their section. This ensures that members can help out if the speaker becomes nervous and loses track of what to say or if they forget something. If each member knows the entire presentation, then there is always someone who can step up and support the speaker by maintaining the narrative and not losing the audience's attention.

Practicing the Presentation

The most critical thing to do before giving a group presentation is to practice as a group. Rehearse what will be said and how it will be said so you know that the overall structure works, that the time is allotted correctly, and that any changes can be made, if needed. Also, rehearsing the presentation should include practicing use of the technology and choreographing where people will stand. An effective strategy is to rehearse the entire presentation at least twice. Practice with each member taking turns speaking in front of the other members pretending that they are the audience. This way the group members can take turns offering suggestions about improving the presentation and the speaker gets more comfortable speaking in front of people. Practice a second time presenting as a group. This way, everyone can rehearse where to stand and coordinate transitions. If possible, practice in the room where your presentation will take place; standing in the front of a classroom feels very different from sitting there as a student.

During the Presentation

Before the Presentations Begin

If groups are presenting from a shared computer, ask your professor if you could pre-load your slides or other visual aids before the class begins . This will ensure that you're not taking time away from your presentation downloading and setting everything up. In addition, if there is a problem, it can be resolved beforehand rather than it being a distraction when you start the presentation.

Introduction

Begin by having the moderator introduce the group by giving each member's name and a brief description of what they will be presenting on. And, yes, this seems like a pointless formality because it's likely that everyone knows everyone else. However, this is expected because it reflects giving oral presentations in most professional and work settings. In addition, your group has a limited amount of time to present and introducing everyone before the presentation begins saves more time than having each individual introduce themselves before they speak.

When Not Speaking

Assuming your group has practiced at least twice [and preferably more], you have heard and seen the entire presentation multiple times. Keep in mind, however, that your audience has not and they can observe everyone in the group. Be engaged. Do not look bored or distracted while others are speaking. Pay attention to each other by watching what the presenter is doing. Respond positively to the presenter and use nonverbal cues [e.g., nodding your head] as a way to help emphasize keys points of the presentation; audiences notice when those not speaking react to something the speaker is saying.

Coordinate Moving from One Speaker to the Next

The person presenting should take a position in the foreground of where you are delivering the information. Group members not speaking should step back and take a spot behind or off to the side of the speaker. When the person speaking is done, the next person steps forward. This pre-planned choreography may seem trivial, but it emphasizes to your audience who the next speaker will be and demonstrates a smooth, coordinated delivery throughout the presentation.

Visual Aids

Plan ahead how to use slides or other visual aids. The person currently presenting should not be distracted by having to constantly move to the next slide, backup and show an earlier slide, or exit a slide to show a video or external web page . Coordinate who in the group is responsible for taking the cue to change slides or otherwise manipulate the technology. When it's time for that person to speak, have a plan in place for passing this responsibility to someone else in the group. Fumbling around with who does what when, distracts the audience. Note however that the role of moving from one slide to the next does not count as being a presenter!

The presentation should conclude with the moderator stepping forward and thanking the audience and asking if there are any questions. If a question relates to a specific part of the presentation, the group member who spoke during that part should answer the question; it should not be the moderator's responsibility to answer for everyone. If another group follows your presentation from a shared computer, be courteous and close out all of your slides or other visual aids before stepping away.

Aguilera, Anna, Jesse Schreier, and Cassandra Saitow. "Using Iterative Group Presentations in an Introductory Biology Course to Enhance Student Engagement and Critical Thinking." The American Biology Teacher 79 (August 2017): 450-454; Barnard, Sam. "Guide for Giving a Group Presentation." VirtualSpeech Ltd., 2019; Eisen, Arri. "Small-Group Presentations: Teaching Science Thinking and Context in a Large Biology Class." BioScience 48 (January 1998): 53-58; Group Presentations. Writing@CSU. Colorado State University ; Kågesten, Owe, and Johann Engelbrecht. "Student Group Presentations: A Learning Instrument in Undergraduate Mathematics for Engineering Students." European Journal of Engineering Education 32 (2007): 303-314; Lucas, Stephen. The Art of Public Speaking . [Chapter 19]. 12th edition. Boston, MA: McGraw-Hill Higher Education, 2015; McArthur, John A. “10 Tips for Improving Group Presentations.” [blog]. Department of Communication Studies, Furman University, November 1, 2011; Melosevic, Sara. “Simple Group Presentation Tips for Maximum Teamwork Magic.” PresentBetter, November 13, 2018; St. John, Ron. Group Project Guidelines. Department of Speech, University of Hawai'i Maui Community College, January 16, 2002.

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How to Present to an Audience That Knows More Than You

  • Deborah Grayson Riegel

introducing group in presentation

Lean into being a facilitator — not an expert.

What happens when you have to give a presentation to an audience that might have some professionals who have more expertise on the topic than you do? While it can be intimidating, it can also be an opportunity to leverage their deep and diverse expertise in service of the group’s learning. And it’s an opportunity to exercise some intellectual humility, which includes having respect for other viewpoints, not being intellectually overconfident, separating your ego from your intellect, and being willing to revise your own viewpoint — especially in the face of new information. This article offers several tips for how you might approach a roomful of experts, including how to invite them into the discussion without allowing them to completely take over, as well as how to pivot on the proposed topic when necessary.

I was five years into my executive coaching practice when I was invited to lead a workshop on “Coaching Skills for Human Resource Leaders” at a global conference. As the room filled up with participants, I identified a few colleagues who had already been coaching professionally for more than a decade. I felt self-doubt start to kick in: Why were they even here? What did they come to learn? Why do they want to hear from me?

introducing group in presentation

  • Deborah Grayson Riegel is a professional speaker and facilitator, as well as a communication and presentation skills coach. She teaches leadership communication at Duke University’s Fuqua School of Business and has taught for Wharton Business School, Columbia Business School’s Women in Leadership Program, and Peking University’s International MBA Program. She is the author of Overcoming Overthinking: 36 Ways to Tame Anxiety for Work, School, and Life and the best-selling Go To Help: 31 Strategies to Offer, Ask for, and Accept Help .

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Fundamental groups and group presentations with bounded relator lengths

  • Original Paper
  • Open access
  • Published: 10 May 2024
  • Volume 218 , article number  80 , ( 2024 )

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introducing group in presentation

  • Sergio Zamora   ORCID: orcid.org/0000-0003-3394-8669 1  

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We study the geometry of compact geodesic spaces with trivial first Betti number admitting large finite groups of isometries. We show that if a finite group G acts by isometries on a compact geodesic space X whose first Betti number vanishes, then \({\text {diam}}(X) / {\text {diam}}(X / G ) \le 4 \sqrt{ \vert G \vert }\) . For a group G and a finite symmetric generating set S , \(P_k(\varGamma (G, S))\) denotes the 2-dimensional CW-complex whose 1-skeleton is the Cayley graph \(\varGamma \) of G with respect to S and whose 2-cells are m -gons for \(0 \le m \le k\) , defined by the simple graph loops of length m in \(\varGamma \) , up to cyclic permutations. Let G be a finite abelian group with \(\vert G \vert \ge 3\) and S a symmetric set of generators for which \(P_k(\varGamma (G,S))\) has trivial first Betti number. We show that the first nontrivial eigenvalue \(-\lambda _1\) of the Laplacian on the Cayley graph satisfies \(\lambda _1 \ge 2 - 2 \cos ( 2 \pi / k ) \) . We also give an explicit upper bound on the diameter of the Cayley graph of G with respect to S of the form \(O (k^2 \vert S \vert \log \vert G \vert )\) . Related explicit bounds for the Cheeger constant and Kazhdan constant of the pair ( G ,  S ) are also obtained.

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Avoid common mistakes on your manuscript.

1 Introduction

1.1 diameter.

Compact geodesic spaces equipped with large discrete groups of isometries have been objects of great interest for a long time and several problems can be formulated in this setting [ 5 , 9 , 21 , 22 , 36 ]. One natural source of such spaces are finite-sheeted Galois covers of compact Riemannian manifolds. In 2009, Petrunin asked if one can control in an interesting way the diameter of a compact universal cover [ 32 ].

(Petrunin) Let M be a compact Riemannian manifold and assume it admits a compact universal cover \({\tilde{M}}\) . What is the smallest upper bound of \({\text {diam}}({\tilde{M}}) / {\text {diam}}(M)\) in terms of \(\vert \pi _1(M) \vert \) ?

It is not hard to show that \({\text {diam}}({\tilde{M}})/ {\text {diam}}(M) \le \vert \pi _1( M ) \vert \) [ 31 ], but getting a better bound is non-trivial matter. The goal of this paper is to study this question and the global shape of compact universal covers in general. One of our main results is the following.

Let X be a compact geodesic space and \(G \le {\text {Iso}}(X)\) a finite group of isometries. If the first Betti number \({\text {b}_1}(X)\) vanishes, then

Asymptotically as \(\vert G \vert \rightarrow \infty \) , there is a stronger yet non-effective bound [ 5 ].

(Benjamini–Finucane–Tessera) Let \(X_n \) be a sequence of compact geodesic spaces and \(G_n \le {\text {Iso}}(X_n) \) a sequence of finite groups with \(\vert G_n \vert \rightarrow \infty \) as \(n\rightarrow \infty \) . If the first Betti numbers \({\text {b}_1}(X_n)\) vanish, then for each \(\varepsilon > 0\) one has

Problem  1 is better handled when reformulated in terms of Cayley graphs. For a group G and a finite symmetric generating set S we denote by \(\varGamma (G, S)\) the Cayley graph of G with respect to S .

For a graph \(\varGamma \) and an integer \(k \in \mathbb {N}\) , as in [ 18 ] we denote by \(P_k(\varGamma )\) the 2-dimensional CW-complex whose 1-skeleton is \(\varGamma \) and whose 2-cells are m -gons for \(0 \le m \le k\) , defined by the simple graph loops of length m in \(\varGamma \) , up to cyclic permutations.

Proposition 4

(Švarc–Milnor Lemma) Let X be a proper geodesic space, \(p \in X\) , \(G \le {\text {Iso}}(X)\) a discrete group, \(\delta \ge 0\) , and \(r \ge 2 \cdot {\text {diam}}(X/ G) + \delta \) . Then \( S: = \{ g \in G \, \vert \, d(gp,p) \le r \} \) generates G . Moreover, if we equip G with the metric induced from \(\varGamma := \varGamma (G,S)\) , for all \(g, h \in G\) one has

Proposition 5

Let X and \(\varGamma \) be as in Proposition  4 . Then \(\pi _1(P_3(\varGamma ))\) is a quotient of \(\pi _1(X)\) .

A proof of the Švarc–Milnor Lemma can be found in [ 17 ], and Proposition  5 will be proven in Sect.  3.3 . Using these well known results, Theorem  2 becomes a corollary of its Cayley graph counterpart.

Let \(k \ge 3\) , G be a finite group, and \(S \subset G\) a finite symmetric set of generators for which \( P_k( \varGamma (G,S) ) \) has trivial first Betti number. Then

It is well known that for \(k \ge 3\) , a group G and a finite symmetric set of generators S , the complex \(P_k (\varGamma (G,S))\) is simply connected if and only if G admits a presentation \(\langle S \, \vert \, R \rangle \) with R consisting of words of length \(\le k\) [ 18 , Section 2] Footnote 1 Moreover, if one considers the abstract group \({\tilde{G}} = \langle S \, \vert \, R_k \rangle \) , where \(R_k\) consists of the words of length \(\le k\) representing the identity in G , then \(P_k (\varGamma ({\tilde{G}}, S))\) is the universal cover of \(P_k (\varGamma (G,S))\) and the fundamental group of \(P_k (\varGamma (G,S))\) is precisely the kernel of the natural map \({\tilde{G}} \rightarrow G\) .

By Remark  7 , Theorem 6 has the following implication.

Corollary 8

Let \(k \ge 3\) , G be a finite group, and \(S \subset G\) a finite symmetric set of generators for which G admits a presentation \(\langle S \, \vert \, R \rangle \) with R consisting of words of length \(\le k\) . Then ( 1 ) holds.

1.2 Kazhdan constant, Cheeger constant, and spectral gap

The Švarc–Milnor Lemma implies that the medium-scale geometric features of X and \(\varGamma \) are closely related to each other. We now focus on such properties. Recall that for a finite group G and a finite symmetric set of generators S , the Kazhdan constant K ( G ,  S ), Cheeger constant h , and spectral gap \(\lambda _1\) are related by the following inequalities

We refer the reader to Sect.  3.5 for the definition of such quantities and further comments on ( 2 ). For now we just mention that the three non-negative quantities K ( G ,  S ), h , and \(\lambda _1\) measure the connectivity of \(\varGamma (G,S)\) in different ways. The other main result of this paper concerns finite abelian groups.

Let \(k \ge 3\) , G a finite abelian group with \(\vert G \vert \ge 3\) , and \(S\subset G\) a symmetric set of generators for which \( P_k (\varGamma (G, S))\) has trivial first Betti number. Then the Kazhdan constant satisfies

Consequently, the Cheeger constant, spectral gap, and diameter satisfy

A consequence of Theorem  9 is an upper bound on the mixing time of the walk in the corresponding Cayley graph (see Remark  33 ). We refer the reader to Sect.  3.6 for the definitions of random walk and mixing time. For now we just mention that \(\tau _{\varGamma } (c)\) is an estimate of how long does one have to wait for heat to propagate evenly (how evenly? quantified by c ) along the network \(\varGamma \) .

Corollary 10

Let \(k \ge 4\) , G , and S be as in Theorem 9 . If \(\tau _{\varGamma }: [0,2] \rightarrow \mathbb {N}\) denotes the mixing time of the Cayley graph \(\varGamma (G,S)\) , then

Theorem  9 also yields an effective bound on the diameter of the universal cover of a closed Riemannian manifold with finite abelian fundamental group.

Corollary 11

Let M be a closed n -dimensional Riemannian manifold with \(\text {diam} (M)\) \( =D\) , Ricci curvature \(\ge \kappa (n-1)\) for some \(\kappa \in \mathbb {R}\) , and having a point whose injectivity radius is \(\ge 2 r_0 > 0 \) . If its fundamental group \(\pi _1 (M)\) is finite and abelian, then the universal cover \({\tilde{M}}\) satisfies

where \(v_n^{\kappa }(r) \) denotes the volume of a ball of radius r in the n -dimensional simply connected space of constant sectional curvature \(\kappa \) .

Considering the situation when \({\text {diam}}(\varGamma ) \rightarrow \infty \) , there are bounds similar to the ones in Theorem  9 for groups that are not necessarily abelian [ 9 ].

(Breuillard–Tointon) Let \(G_n\) be a sequence of finite groups, \(S_n \subset G_n \) a sequence of finite symmetric sets of generators, and \(\varGamma _n: = \varGamma (G_n, S_n)\) the corresponding Cayley graphs. Assume there is a sequence \(k_n = o ({\text {diam}}(\varGamma _n)) \) such that the first Betti numbers \({\text {b}_1}(P_{k_n}(\varGamma _n))\) vanish. Then for each \(\varepsilon > 0 \) , the quantities

cannot go to zero faster than \((\vert S _n \vert / \vert G _n \vert )^{\varepsilon }\) as \(n \rightarrow \infty \) .

1.3 Outline

In Sect.  2 we present some computations and examples, and discuss related open problems and potential lines of research.

In Sect.  3 we introduce our notation and the standard theory we will need.

In Sect.  4 we give the proofs of Theorems 2 and 6 . Theorem 2 follows from Theorem 6 which in turn depends on an elementary combinatorial argument. We also present a proof of Theorem  3 since it is currently stated in the literature only in the setting of vertex-transitive graphs [ 5 , Theorem 1].

In Sect.  5 we give the proofs of Theorem 9 and Corollaries  10 and 11 . An elementary geometric observation yields estimate ( 3 ), from which all other results follow.

2 Examples and further problems

2.1 diameter.

Theorem  3 implies that the explicit bound in Theorem  2 is far from being sharp as \(\vert G \vert \rightarrow \infty \) . By a fundamental domain argument, even without the first Betti number assumption, one always has

so Theorem  2 says nothing new for \(\vert G \vert \le 4\) . However, for a larger number, say, 120, Theorem 2 gives a meaningful bound (again, likely far from sharp). The following example was pointed out by Kuperberg [ 32 ].

Let \({\tilde{X}} = \mathbb {S}^3\) equipped with its usual metric, and consider \(X = ({\tilde{X}}/\sim )\) the Poincaré sphere [ 35 , Example 1.4.4 and Problem 4.4.17]. Then \({\tilde{X}}\) is the 120-sheeted universal cover of X , and

where \(\varphi \) is the golden ratio. On the other hand, the bound provided by Theorem  2 is \(4\sqrt{120} \approx 43.81\) .

Proof sketch A Voronoi domain of the quotient \({\tilde{X}} \rightarrow X\) is a regular dodecahedron \(K \subset \mathbb {S}^3\) with dihedral angles equal to \(\pi /3\) [ 30 , Section 3.2.4]. Let \(O\in K\) be the center of the dodecahedron, \(F_1,\) \( F_2\) be the centers of two adjacent faces of K , and \(V_1,\) \(V_2\) be the vertices shared by such faces. Also let P be the midpoint between \(V_1\) and \(V_2\) . The diameter of X is attained by \(d_{\mathbb {S}^3}(O, V_1)\) (see Fig.  1 ).

figure 1

We can use the knowledge of the angles in the triangle \(OF_1P\) to deduce the length of the segment OP . We then proceed to compute the length of the segment \(OV_1\) using the length of the segment OP and the known angles of the triangle \(OPV_1\)

By the symmetry of the dodecahedron,

Using elementary geometry one can also compute the angles

By the spherical laws of sines and cosines, this is enough information to recover the length \(d_{\mathbb {S}^3}(O, V_1) = \arccos ( \varphi ^2 / \sqrt{8} )\) .

It would also be interesting to investigate how sharp is Theorem 3 . The known example in which \({\text {diam}}(X_n ) / {\text {diam}}(X_n / G_n )\) grows the fastest with respect to \(\vert G _n\vert \) is the following (again pointed out by Kuperberg [ 32 ]), which naturally leads to Conjecture 15 below.

Let \(G_n \) be the symmetric group (the set of bijections of the set \(\{ 1, \ldots , n \}\) ), and \(S_n\) the set of transpositions of consecutive elements of \(\{1, \ldots , n \}\) (we consider n and 1 not to be consecutive). Setting \(\varGamma _ n: = \varGamma (G_n, S_n)\) , we have:

\( P_6 (\varGamma _n) \) is simply connected for all n .

\({\text {diam}}(\varGamma _n) = o \left( \left( \log \vert G _n \vert \right) ^2 \right) \) .

\( \left( \log \vert G _n \vert \right) ^{2- \varepsilon } = o \left( \text {diam} (\varGamma _n) \right) \) for every \(\varepsilon > 0\) .

Proof sketch  1: The group \(G_n \) can be presented as \(\langle S_n \vert R_n \rangle \) , with \(S_n=\{\sigma _1, \ldots ,\) \( \sigma _{n-1} \}\) , and \(R_n \) consisting of the words \(\sigma _i^2\) for all i , \((\sigma _i\sigma _{i+1})^3\) for all \(i=1, \ldots , n-2\) , and \((\sigma _i \sigma _j)^2\) with \(\vert i-j \vert \ge 2\) . Since each word in \(R_n\) has length \(\le 6\) , the complex \(P_6(\varGamma _n)\) is simply connected.

2 and 3: Every permutation in \(G_n\) can be written as a composition of at most \(n(n-1)/2\) elements in \(S_n\) , where the maximum is achieved by the permutation

that “reverses” the order. This means that

which is of the order of \(n \log n\) .

Conjecture 15

(Petrunin) There is \(C>0\) such that if G is a finite group and S a set of generators for which \(P_3(\varGamma (G,S))\) is simply connected, then

This question draws resemblance to another well known problem [ 2 ].

Conjecture 16

(Babai) There is \(C>0\) such that if G is a finite non-abelian simple group and \(S\subset G\) is any set of generators, then

Note however, that Babai’s Conjecture concerns any set of generators, while Petrunin’s Conjecture is about geometrically chosen sets of generators. It would be interesting to investigate how intertwined these two problems are. For instance, does the hypothesis in Conjecture  15 of \(P_3(\varGamma (G,S))\) being simply connected imply that the graph \(\varGamma (G,S) \) looks like the Cayley graph of a non-abelian simple group? We refer the reader to [ 20 , 24 ] for recent updates on the state of Conjecture  16 .

We would like to also point out that Conjecture 15 is still very interesting when the group G is abelian, in which case C could even be 1. For abelian groups, the known example in which \({\text {diam}}(\varGamma (G,S ))\) grows the fastest with respect to \(\vert G \vert \) is the following (pointed out by Petrunin [ 32 ]).

Let \(G_n = \mathbb {Z} / ( 2^n) \mathbb {Z} \) , and

Setting \(\varGamma _n: = \varGamma (G_n, S_n)\) , we have:

\(P_3(\varGamma _n)\) is simply connected for all n .

\({\text {diam}}(\varGamma _n) = O \left( \log \vert G _n \vert \right) \) .

\(\log \vert G _n \vert = O \left( \text {diam} (\varGamma _n) \right) . \)

Proof sketch  1: The group \(G_n\) can be presented as \(\langle S_n \vert R_n \rangle \) , where \(R_n\) consists of the expressions \( 2^j - 2^{j-1} - 2^{j-1} =0\) for \(j\in \{ 1, \ldots , n-1 \}\) , and \(2^{n-1} + 2^{n-1} = 0\) . Since each word in \(R_n\) has length \(\le 3\) , the complex \(P_3(\varGamma _n)\) is simply connected.

2: Any number in \(\{ 1, 2, 3, \ldots , 2^n -1 \}\) can be written (using binary base) as a sum of at most n summands of the form \(2^j\) , \(j \in \{1, \ldots , n-1\}\) . Hence

3: Given a sequence of length n of 0’s and 1’s, one could count the number of “jumps” from one digit to another. E.g., 0001111 has 1 jump, 0011101 has 3 jumps, 1010110 has 5 jumps, etc. By writing an element \(x \in G_n\) in binary base, we obtain a sequence of length n of 0’s and 1’s. One can check that the effect of adding or substracting a power of 2 to x increases the number of such jumps by at most 2.

Expressing \(x= 1 + 2^2 + \ldots + 2^{2 \lfloor \frac{n-1}{2} \rfloor }\) in binary we find \(n-1\) jumps. Hence at least \(\left\lfloor \frac{n}{2} \right\rfloor \) elements of \(S_n\) are required to write down x . This implies,

We conclude this section by pointing out that examples of spaces X with \({\text {b}_1}(X) = 0\) and finite groups \(G \le {\text {Iso}}(X)\) with \({\text {diam}}(X) / {\text {diam}}(X / G )\) of order \(\log \vert G \vert \) arise in number theory.

(Calegari–Dunfield, Boston–Ellenberg) There is a closed hyperbolic 3-manifold \(M_0\) admitting a tower of regular \(m_n\) -sheeted covers \(M_n \rightarrow M_0\) with \({\text {b}_1}(M_n) = 0\) for all n , and

for some \(C> c > 0\) .

Proof sketch: In [ 15 , Theorem 1.6], a sequence of regular finite-sheeted covers \(M_n \rightarrow M_0\) is constructed, with \(M_0\) a quotient of the hyperbolic space \(\mathbb {H}^3\) by an arithmetic lattice \(\varGamma \le PGL_2(\mathbb {C})\) , which possesses the Selberg property (see [ 27 , Section 2]).

Since these covers correspond to congruence subgroups of \(\varGamma \) , by the Selberg property their (analytic) spectral gaps satisfy \(\lambda _1 (M_n) \ge \varepsilon \) for some \(\varepsilon > 0\) . Then by the work of Brooks [ 12 , Theorem 1], the estimates ( 6 ) follow.

In [ 7 ] it was then proven that \({\text {b}_1}(M_n) = 0\) for all n (this fact was proven initially in [ 15 ] assuming the Generalized Riemann Hypothesis and Langlands-type conjectures).

2.2 Spectral gap

The bounds in Theorem  9 and Corollary 10 are rather general, so we don’t expect them to be fully sharp.

Let \(G_n = (\mathbb {Z}/ 2 \mathbb {Z})^n\) , \(S_n = \{ e_i \in G_n \vert i \in \{ 1, \ldots , n \} \} \) , where \(e_i\) is the i -th basis vector, and \(\varGamma _n = \varGamma (G_n, S_n)\) . Then \(P_4(\varGamma _n)\) is simply connected for each n so by Corollary 10

For fixed \(c>0\) , this bound grows quadratically in n . However, a careful computation [ 19 ] shows that

Let \(G_n = \mathbb {Z}/n\mathbb {Z}\) , \(S_n = \{ -1,1 \} \) , and \(\varGamma _n = \varGamma (G_n, S_n)\) . For fixed \(\varepsilon >0\) , consider the sequence

By the Central Limit Theorem [ 1 , Section 7.3], the random walk in \(\varGamma _n\) after \(t_n\) steps will be concentrated in the interval \([-n/\sqrt{t_n}, n/\sqrt{t_n}]\) . That is,

This implies that for fixed \(c <2 \) , and large enough n ,

Notice \(P_n(\varGamma _n)\) is simply connected for each n , so the bound given by Corollary  10 is the following, not far from being sharp:

It would be desirable to find explicit bounds similar to the ones of Theorem  9 in the non-abelian setting. However, at the moment the topological condition of \(P_k(\varGamma (G,S))\) having trivial first Betti number (or even being simply connected) seems very hard to use when studying isometric actions \(G \rightarrow {\text {Iso}}(\mathbb {S}^n)\) with \(n \ge 2\) . In this direction, there is a universal control on the diameters of quotients of spheres by group actions [ 22 ].

(Gorodski–Lange–Lytchak–Mendes) There is \(\delta > 0 \) such that for any \(n \ge 2\) and any compact group \(G \le {\text {Iso}}(\mathbb {S}^n)\) not acting transitively, one has

With techniques similar to the ones in the work of Mantuano [ 29 ], it seems possible to recover, using Theorem 9 , effective estimates on spectral gaps and medium-scale isoperimetric inequalities for compact Riemannian manifolds with trivial first Betti number and actions by finite abelian groups with small quotient. Successful results in similar programs have been obtained by Brooks [ 10 , 11 ], Buser [ 14 ], Burger [ 13 ], Magee [ 28 ], and several others, mostly for surfaces.

2.3 (Lack of) Gromov–Hausdorff precompactness

An interesting problem in the theory of finite groups was to understand the possible limits of finite homogeneous spaces. For instance; can one find a sequence of compact geodesic spaces \(X_n\) and finite groups \(G_n \le {\text {Iso}}(X_n)\) with \({\text {diam}}(X_n / G_n )\rightarrow 0\) such that \(X_n\) converges to \(\mathbb {S}^2\) in the Gromov–Hausdorff sense? This question was answered negatively by Turing [ 36 ], and building upon his work, Gelander [ 21 ] proved the following.

(Gelander) Let \(X_n\) be a sequence of compact geodesic spaces and \(G_n \le {\text {Iso}}(X_n)\) a sequence of finite groups with \({\text {diam}}(X_n /G_n ) \rightarrow 0\) . If \(X_n\) converges in the Gromov–Hausdorff sense to a compact space X , then X is a (possibly infinite-dimensional) torus.

A consequence of Theorem  22 is that a sequence of normalized universal covers cannot have a “limit shape”.

Corollary 23

Let \(X_n\) be a sequence of compact geodesic spaces and \(G_n \le {\text {Iso}}(X_n)\) a sequence of finite groups with \({\text {diam}}(X_n/G_n) / {\text {diam}}(X_n) \rightarrow 0 \) . If \({\text {b}_1}(X_n) = 0\) for all n , then the sequence \(X_n / {\text {diam}}(X_n)\) diverges in the Gromov–Hausdorff sense.

Assuming the contrary, \(X_n / {\text {diam}}(X_n)\) converges to a space X of diameter 1. By Theorem  22 , X is a torus so it admits a regular covering with Galois group \(\mathbb {Z}\) . Then by the work of Sormani–Wei [ 34 , Theorem 3.4], there are surjective morphisms \(\pi _1 (X_n) \rightarrow \mathbb {Z}\) for n large enough contradicting the assumption \({\text {b}_1}(X_n) = 0\) . \(\square \)

Theorems  3 and  12 are proven in a similar fashion. In [ 5 , 9 ], building upon the structure of approximate groups by Breuillard–Green–Tao [ 8 ], it is proven that if one had contradicting subsequences, then the normalized spaces would converge to a finite-dimensional torus, contradicting the lower-semi-continuity of the first Betti number [ 34 ].

It would be interesting to further understand what causes the behavior of the sequences \(X_n / {\text {diam}}(X_n)\) in Corollary 23 . Recall that some known families of Gromov–Hausdorff divergent sequences such as \(X_n = \mathbb {S}^n\) or \(X_n = (\mathbb {Z}/2\mathbb {Z})^n\) present a concentration of measure property [ 25 ].

Definition 25

We say that a sequence \((X_n, d_n, \mu _n )\) of metric probability spaces of diameter 1 is a Levy family if for any sequence of 1-Lipschitz maps \(f_n: X_n \rightarrow \mathbb {R}\) , the sequence of variances \( \text {Var} \left( (f_n )_{*} \mu _n \right) \) goes to 0 as \(n \rightarrow \infty \) .

Conjecture 26

(Petrunin) Let \((X_n, d_n, \mu _n )\) be a sequence of compact simply connected geodesic probability spaces and \(G_n \le {\text {Iso}}(X_n)\) a sequence of finite groups of measure preserving isometries with \({\text {diam}}(X_n / G_n) \rightarrow 0\) . Then \(X_n\) is a Levy family.

3 Preliminaries

3.1 notation.

For a finite-dimensional \(\mathbb {C}\) -Hilbert space V , we denote by \( {\text {End}}(V)\) the space of linear maps \(V \rightarrow V\) and by \(U (V) \subset {\text {End}}(V) \) the set of unitary automorphisms. If \(V = \mathbb {C}^n\) , then we denote U ( V ) also by U ( n ). For \(A \in {\text {End}}(V) \) , we denote its spectrum by \(\sigma (A) \subset \mathbb {C}\) and its adjoint by \(A^{*}\) . The trace operator is denoted by \( {\text {Tr}}: {\text {End}}(V ) \rightarrow \mathbb {C} \) . When V is 1-dimensional, we will identify \({\text {End}}(V )\) with \(\mathbb {C}\) via \({\text {Tr}}: {\text {End}}(V ) \rightarrow \mathbb {C}\) .

For a path connected topological space X , we denote its first Betti number by \({\text {b}_1}(X)\) . Recall that it equals the supremum of the m for which there is a surjective morphism \(\pi _1(X) \rightarrow \mathbb {Z}^m\) .

For a metric space X , \(p \in X\) , and \(r > 0 \) , we denote by B ( p ,  r ) the open ball of radius r around p . For two metric spaces X and Y , we denote their Gromov–Hausdorff distance by \(d_{GH}(X,Y)\) .

3.2 Graphs and CW-complexes

For the purposes of this paper, a graph always means a locally finite undirected graph without loops or multiple edges. For vertices x ,  y in a graph, we write \(x \sim y\) if there is an edge connecting x to y . For an edge [ x ,  y ], we denote by ( x ,  y ) its interior.

For a sequence of vertices \(v_0, v_1, \ldots , v_m\) in a graph \(\varGamma \) such that \(v_{i-1} \sim v_i\) for each \(i \in \{ 1, \ldots , m \}\) , we denote by \([ v_0, \ldots , v_m ] \) the curve \(\gamma : [0,m] \rightarrow \varGamma \) with \(\gamma (i) = v_i\) for every \(i \in \{ 0, \ldots , m \}\) , so that \(\gamma | _{[i-1,i]} \) travels along the edge \(v_{i-1}v_i\) . A curve (loop) of this form is called a graph curve (loop) of length m .

For vertices x ,  y in a connected graph \(\varGamma \) , the graph distance \(d_{\varGamma }(x,y)\) between x and y is the minimum m for which there is a graph curve of length m connecting them.

For a graph \(\varGamma \) and an integer \(k \in \mathbb {N}\) , we denote by \(P_k(\varGamma )\) the 2-dimensional CW-complex whose 1-skeleton is \(\varGamma \) and whose 2-cells are m -gons for \(0 \le m \le k\) , defined by the simple graph loops of length m in \(\varGamma \) , up to cyclic permutations.

It is not hard to equip \(P_k(\varGamma )\) with a geodesic metric that restricted to \(\varGamma \) coincides with its original metric, and such that \(d_{GH}(P_k(\varGamma ), \varGamma ) \le k \) . For instance; for \(k=3\) one can make each 2-cell a Reuleaux triangle.

Let G be a group and \(S \subset G\) a symmetric generating subset. The Cayley graph \(\varGamma (G,S)\) of G with respect to S is defined to be the one with G as its vertex set and such that two distinct elements \(g, h \in G\) are adjacent if and only if \(g = hs\) for some \(s \in S\) .

We now state a trivial observation. We include its proof since this same counting argument will be used later (see Claim 2 in the proof of Theorem  6 ).

Let G be a finite group with \(\vert G \vert \ge 3\) , \(S \subset G\) a symmetric set of generators, \(\varGamma : = \varGamma (G, S)\) the Cayley graph, and \(t \in S \backslash \{ e \} \) . Then \(\varGamma \backslash (e,t ) \) is connected.

If t has order \(m \ge 3\) , then the path \([t,t^2, \ldots , t^m ]\) connects the endpoints of the removed edge, so we can assume \(t =t^{-1}\) . Let \(C_1 \) and \(C_2\) denote the connected components of \(\varGamma \backslash (e,t)\) containing e and t , respectively. Since multiplication by t exchanges e and t , it sends \(C_1\) to \(C_2\) and vice-versa, so \(\vert C_1 \vert = \vert C_2 \vert \) .

Since \(\vert G \vert \ge 3\) , \(S \backslash \{ e \}\) contains an element \(s \ne t\) . Multiplication by s sends ( e ,  t ) to ( s ,  st ), so \(s C_1\) is the connected component of \(\varGamma \backslash (s,st) \) containing s . Since \(s \ne t = t^{-1}\) , the three segments ( s ,  e ), ( s ,  st ), and ( e ,  t ) are distinct. Hence,

The path [ s ,  e ,  t ] lies entirely in \(sC_1\subset \varGamma \backslash (s,st)\) .

The path [ e ,  s ,  st ] lies entirely in \(C_1 \subset \varGamma \backslash (e,t)\) .

If \(C_1 \ne C_2\) , then \(C_1 \cap C_2 = \emptyset \) and the above implies that

The connected set \( [s,e,t] \cup C_2\) lies entirely in \(sC_1 \subset \varGamma \backslash (s,st)\) .

\(\{ s, e \} \cap C_2 = \emptyset \) .

This contradiction finishes the proof of Lemma 28 . \(\square \)

3.3 Constructing covering spaces

In this section we prove Proposition 5 . In order to do so, we present a general construction (cf. [ 23 , Section 5D]).

Proposition 29

Let X be a proper geodesic space, \(p \in X\) , \(G \le {\text {Iso}}(X)\) a discrete group of isometries, and \(r \ge 2 \cdot {\text {diam}}(X/ G)\) . Then set \(S: = \{ g \in G \vert d(gp,p ) \le r \}\) , and let \(\tilde{G}\) be the abstract group generated by S , with relations

\(s= s_1 s_2\) in \( \tilde{G} \) , whenever \(s, s_1, s_2 \in S\) and \(s= s_1s_2\) in G .

Denote the canonical embedding \(S \hookrightarrow \tilde{G} \) as \((s \rightarrow s^{\sharp } )\) , and by \(\varPhi : \tilde{G} \rightarrow G\) the unique morphism with \(\varPhi (s^{\sharp }) = s\) for all \(s \in S\) . Then there is a regular covering \(\tilde{X} \rightarrow X\) with Galois group \({\text {Ker}}(\varPhi )\) .

Proof    In order to construct the space \(\tilde{X}\) , notice that by discreteness of G , there is \(\eta > 0 \) with \( S = \{ g \in G \vert d(gp,p ) < r + 2 \eta \} \) . Set \(B : = B(p, r/2 + \eta ) \) . Then \(S = \{ g \in G \vert B \cap gB \ne \emptyset \}\) . Equip \( \tilde{G} \) with the discrete topology, and consider the topological space

\(\tilde{X} := \left( \tilde{G } \times B \right) / \sim \) ,

where \(\sim \) is the minimal equivalence relation such that

We then obtain a continuous map \(\varPsi : \tilde{X} \rightarrow X\) given by

\(\varPsi (g, x) : = \varPhi (g)(x) .\)

Fix \(g _0 \in \tilde{G} \) and set \(U : = \varPhi (g_0) (B)\) . The proof of [ 37 , Theorem 2.32] carries over (with \(V = B\) and \(\varGamma = G\) ) to show that U is evenly covered. As \(g_0\) ranges over \(\tilde{G}\) , the sets \(\varPhi (g_0)(B)\) cover X , so \(\varPsi \) is a covering map. The proof of [ 37 , Theorem 2.32] again carries over to show that \(\varPsi \) is regular with Galois group \({\text {Ker}}(\varPhi )\) .

We now prove Proposition 5 . Let \(X, G, S, \varGamma \) be as in the statement of the proposition. Let \(\tilde{G}\) be the group with presentation \( \langle S \, \vert \, R \rangle \) , where R consists of the words of length \(\le 3\) that represent the trivial element of G . Then \(P_3(\varGamma (\tilde{G}, S))\) is the universal cover of \(P_3(\varGamma )\) , and \(\pi _1(P_3(\varGamma ))\) is isomorphic to the kernel of the natural map \(\tilde{G} \rightarrow G\) (see Remark 7 ). By Proposition 29 , there is a regular covering map \(\tilde{X} \rightarrow X\) with Galois group \(\pi _1(P_3(\varGamma ))\) , so there is a surjective map \(\pi _1(X) \rightarrow \pi _1(P_3(\varGamma ))\) .

3.4 Representation theory of finite groups

In this section we recall the results from representation theory we will need. We refer the reader to [ 33 , Chapters 1-2] for proofs and further discussion. Throughout this section, let G be a finite group.

For our purposes, a (unitary) representation is a morphism \(\rho : G \rightarrow U (V) \) for some finite-dimensional \(\mathbb {C}\) -Hilbert space V . The dimension of V is called the dimension of the representation and will be denoted by \(d_{\rho }\) . We say that such representation is irreducible if whenever there is a subspace \(W \le V\) invariant under the G -action, either \(W = \{ 0 \}\) or \(W = V\) . The representation \(\rho \) is said to be trivial if \(\rho (g) = {\text {Id}}_V\) for all \(g \in G\) .

Given two representations \(\rho _ 1: G \rightarrow U (V_1)\) , \(\rho _2: G \rightarrow U (V_2)\) , we say a linear map \(\lambda : V_1 \rightarrow V_2\) is equivariant if

We say that \(\rho _1\) and \(\rho _2\) are isomorphic if there is an equivariant linear isomorphism \(\lambda : V_1 \rightarrow V_2\) . It turns out there are only finitely many isomorphism classes of irreducible representations and they satisfy

where the sum is taken among the isomorphism classes of irreducible unitary representations of G .

Let \(\mathbb {C}[G]\) be the space of functions \(G \rightarrow \mathbb {C}\) . For \(f \in \mathbb {C}[G]\) , we denote by \(f^{*} \in \mathbb {C}[G] \) the function given by \(f ^{*}(g): = \overline{f(g^{-1})}\) . For \(f, h \in \mathbb {C}[G]\) , their product is defined as

The Hermitian product

makes \(\mathbb {C}[G]\) a Hilbert space called the convolution algebra of G . It admits a natural action \(\rho _0: G \rightarrow U ( \mathbb {C}[G])\) given by

For \(f \in \mathbb {C}[G]\) and a representation \(\rho : G \rightarrow U(V)\) , the Fourier transform \({\hat{f}}(\rho ) \in {\text {End}}(V)\) is defined as

The Fourier transform is compatible with products and adjoints. That is,

for any \(f, h \in \mathbb {C}[G]\) and any representation \(\rho \) .

It can be shown that for any irreducible representation \(\rho : G \rightarrow U (V)\) , there is a (non-unique!) equivariant isometric embedding \( \iota _V: V \rightarrow \mathbb {C} [G]\) . Moreover, such embeddings among all irreducible representations span \(\mathbb {C}[G]\) . This leads to the following important result.

(Plancherel formula) For \(f, h \in \mathbb {C}[G]\) one has

The following result follows from the fact that any unitary representation is totally reducible.

For any unitary representation \(\rho : G \rightarrow U (V)\) , there is \(x \in V\) with \(\vert x \vert = 1 \) such that the span of the G -orbit of x is irreducible.

The ensuing result follows from the fact that commuting unitary automorphisms are simultaneously diagonalizable.

Proposition 32

If G is abelian, then any irreducible unitary representation is 1-dimensional.

3.5 Kazhdan constant, Cheeger constant, and spectral gap

We refer the reader to [ 4 ] for a detailed introduction to the theory of Kazhdan’s property (T) and related topics. Throughout this section, let G be a finite group, \(S \subset G\) a symmetric generating set, and \(\varGamma : = \varGamma (G,S)\) the corresponding Cayley graph.

The Kazhdan constant of G with respect to S is defined as

where the first infimum is taken among non-trivial irreducible unitary representations \(\rho : G \rightarrow U (V)\) and the second infimum is taken among unit vectors \(x \in V\) .

The Laplacian is the map \(\varDelta : \mathbb {C}[G] \rightarrow \mathbb {C}[G] \) defined by

This map is equivariant, self adjoint, and its spectrum is a finite set of non-positive real numbers

We denote the \(\varDelta \) -eigenspace of an eigenvalue \(- \lambda \) by \(E_{\lambda }\) . The quantity \(\lambda _1\) is called the spectral gap of G with respect to S .

The Cheeger (isoperimetric) constant of G with respect to S is defined by

where \(\partial A\) denotes the set of edges in \(\varGamma \) connecting a vertex in A with a vertex in \(G \backslash A\) .

The Kazhdan constant K ( G ,  S ) quantifies how easy it is to tell apart isometric actions on spheres with fixed points from isometric actions on spheres without fixed points, the spectral gap \(\lambda _1\) quantifies how fast heat flows through \(\varGamma \) , and h quantifies how bad the bottlenecks of \(\varGamma \) are. Each quantity measures in some way how robust is the network \(\varGamma \) .

Recall that these quantities satisfy the well known relations

(see [ 9 , Section 1.2] for a similar expression involving \({\text {diam}}(\varGamma )\) ). A proof of the first and last inequalities, known as the discrete Cheeger–Buser inequalities, along with historical background can be found in [ 26 , Section 4.2]. To verify the second inequality, take an arbitrary irreducible unitary representation \(\rho : G \rightarrow U (V)\) . Since there exists an equivariant embedding \(\iota _V: V \rightarrow \mathbb {C}[G]\) , we can assume \(V \le \mathbb {C} [V]\) . Moreover, since \(\varDelta \) is equivariant, we can further assume \(V \le E_{\lambda }\) for some \(\lambda \ne 0\) . Then assume a unit vector \(x \in V\) satisfies

for some \(\theta \in [ 0, \pi ] \) . Then the angle between x and \(\rho _0 (s) x\) is at most \( \theta \) for each \(s \in S\) (see Fig.  2 ). This implies

figure 2

Basic trigonometry shows that if the angle between the unit vectors x and \(\rho (s) x\) is \(\theta \) , then the distance between the endpoints is \(2 \sin (\theta / 2)\)

From the identity \( 1 - \cos (\theta ) = 2 \cdot \sin ^2 (\theta / 2) \) , we deduce \([ 2 \cdot \sin (\theta / 2 )]^2 \ge 2 \lambda / \vert S \vert \) . Since x was arbitrary and \(\lambda \ge \lambda _1\) , the second inequality of ( 10 ) follows.

To verify the third inequality of ( 10 ), recall that by Lemma  31 , there is a unit vector \(x \in E_{\lambda _1}\) for which its G -orbit spans an irreducible representation. By definition there is \(t \in S\) with \(d(\rho _0(t)x,x) \ge K (G,S)\) . Set \(K (G,S) = 2 \cdot \sin (\theta /2)\) with \(\theta \in [0, \pi ]\) . Then since \(\vert ( \langle \rho (s) x, x\rangle \vert \le 1 \) for all \(s \in S \backslash \{ t \}\) , one has

3.6 Random walks on Cayley graphs

We refer to [ 19 , Chapter 3] for an introduction on the theory of random walks in finite groups. Throughout this section, let G be a finite group, \(S \subset G\) a symmetric generating set, and \(\varGamma : = \varGamma (G,S)\) the corresponding Cayley graph.

For \(\alpha \ge \vert S \vert \) , the random walk on \(\varGamma \) is the G -valued Markov process \(\{ W^t_{\alpha }\}_{t \in \mathbb {N}} \) such that \(W^0_{\alpha } \equiv e\) , and at each time, if the walker is at \(g \in G\) , then it stays at g with probability \(1 - \vert S \vert / \alpha \) and jumps to a neighbor uniformly at random with probability \(\vert S \vert / \alpha \) . This gives rise to the law

We will denote \(W_{\alpha }^1\) simply by \(W_{\alpha }\) . We can identify \(\mathbb {C}[G]\) with the set of complex valued measures on G via the correspondence

Note that after this identification,

where \(\delta _e\) denotes the Dirac mass at e . It is also straightforward to verify that

for all \(s,t \in \mathbb {N}\) . If \(\alpha > \vert S \vert \) , the distribution \(W^t_{\alpha }\) converges to the uniform distribution U on G as \(t \rightarrow \infty \) . One can quantify how fast this convergence occurs with the quantity

introducing group in presentation

The mixing time \(\tau _{\varGamma }^{\alpha }: [0,2 ] \rightarrow \mathbb {N}\) of the process \(\{ W^t_{\alpha } \}_{t\in \mathbb {N}}\) is defined as

A direct computation shows that for all \(t \in \mathbb {N}\) ,

If \( {\textbf {1}}: G \rightarrow U (1) \) denotes the trivial representation, then ( 9 ) and ( 12 ) imply

for all \(t \in \mathbb {N}\) . Then one has

where the last sum is taken over isomorphism classes of non-trivial irreducible unitary representations; the first equality uses ( 13 ), the second one follows from the Plancherel formula and ( 12 ), and the third one uses ( 14 ). Finally, by the Cauchy-Schwarz inequality, ( 15 ) implies

When \(\alpha = 2 \vert S \vert \) , we denote \(W_{\alpha }^t\) by \(W^t\) , \(W_{\alpha }\) by W , \(\varepsilon _{\alpha }(t)\) by \(\varepsilon (t)\) , and \(\tau _{\varGamma }^{\alpha }\) by \(\tau _{\varGamma }\) .

4 Diameter bounds

In this section we prove Theorems  2 , 3 , and  6 . For a group G and a symmetric generating set \(S\subset G\) , we set \(S_k: = S \cup S^2 \cup \ldots \cup S^{\left\lfloor \frac{k+2}{3} \right\rfloor } \) . It is straightforward to check that

The ensuing result [ 3 ] reduces the proof of Theorem 6 to the case \(k = 3\) .

(Behr) Let G a group, and \(S\subset G\) a finite symmetric set of generators. Then for each \(k \ge 3\) , there is a surjective map

First notice that if an edge \(\omega \) of \(\varGamma (G, S_k) \) corresponds to an element of \(S^m\) with \(m \le \lfloor \frac{k +2 }{3 }\rfloor \) then there is an endpoint-preserving homotopy in \(P_3(\varGamma (G, S_k))\) taking \(\omega \) to a concatenation of m edges in \(\varGamma (G, S)\) (see Fig.  3 ). Since the fundamental group of a CW-complex is generated by the loops in its 1-skeleton, the above observation implies that the inclusion

induces a surjective map at the level of fundamental groups. It remains to check that ( 18 ) extends to a continuous map \(P_k(\varGamma (G,S)) \rightarrow P_3 (\varGamma (G,S_k) ) \) . This boils down to the fact that any word of length \(\le k\) representing the identity in G using the elements of S as letters, can be written as a concatenation of words of length \(\le 3\) representing the identity in G using the elements of \(S_k\) as letters (see [ 16 , Lemma 7.A.8] for further details).

figure 3

If \(\omega = s_1 \cdots s_m\) , then the decomposition \(w = (s_1 \cdots s_{m-1})(s_m)\) yields an endpoint preserving homotopy in \(P_3(\varGamma (G,S_k))\) from w to the concatenation of an edge corresponding to an element in \(S^{m-1}\) and one in S . Proceeding inductively yields the desired homotopy. In the picture \(m = 6\)

\(\square \)

The following elementary observation will be required at the end of the proof of Theorem  6 .

Let \(\varGamma \) be a connected graph, \(T \subset \varGamma \) a connected subgraph, and \(C_1, \ldots , C_{\ell } \subset \varGamma \) the connected components of \(\varGamma \backslash T\) . Then for each \(j \in \{ 1, \ldots , \ell \}\) , the graph \(\varGamma \backslash C_j\) is connected.

If the result is false, there are \(w_0, w_1 \in \varGamma \backslash C_j\) such that any path connecting them passes through \(C_j\) . Since \(\varGamma \) is connected, there is a path \([w_0 = v_0, v_1, \ldots , v_k = w_1]\) , which by assumption passes through \(C_j\) . Let \(i_1\) be the first index such that \(v_{i_1 + 1} \) is in \(C_j\) and let \(i_2\) be the last index such that \(v_{i_2 - 1}\) lies in \(C_j\) . Then both \(v_{i_1}\) and \(v_{i_2}\) lie in T , and by connectedness of T there is a path \([v_{i_1} = a_0, a_1, \ldots , a_{m} = v_{i_2} ]\) in T . Then it is easy to check that the path

does not intersect \(C_j\) , contradicting our assumption (see Fig.  4 ).

figure 4

The portion \([v_{i_1}, v_{i_1+1}, \ldots , v_{i_2-1}, v_{i_2}]\) can be replaced by \([a_0, \ldots , a_m]\) . In the picture the shadowed region represents \(C_j\) , the solid line represents T , \(i_1 = 4\) , and \(i_2=9\)

By Lemma  34 we have \({\text {b}_1}( P_3(\varGamma (G, S_k)) ) = 0 \) . Combining this with ( 17 ) we can assume \(k = 3\) without loss of generality.

Let \(e \in G\) be the neutral element and \(\varGamma = \varGamma (G,S)\) . Take \(h\in G\) with \(d_{\varGamma }(h,e)= m = {\text {diam}}(\varGamma )\) and a minimizing path \( [ e=g_0,g_1, \ldots , g_m=h ] \) . For each i , set \(\varSigma _i \subset \varGamma \) as the subgraph induced by the set of vertices \(\{ g \in G \mid d_{\varGamma } (g,e) = i \}\) and let \(T_i\) be the connected component of \(\varSigma _i\) containing \(g_i\) .

Claim 1: For each \(i_0 \in \{ 1, \ldots , m-1 \}\) , the vertices e and h lie in

distinct connected components of \(\varGamma \backslash T_{i_0}\) .

Let \(Y_0 = Y_1 \subset \varGamma \) be the subgraph induced by \(\bigcup _{j=0}^{i_0-1} \varSigma _ j \) , \(Y_{1/4} \subset \varGamma \) the subgraph induced by \(T_{i_0}\) , \(Y_{1/2} \subset \varGamma \) the subgraph induced by \(\bigcup _{j=i_0 + 1}^m \varSigma _j\) , and \(Y_{3/4} \subset \varGamma \) the subgraph induced by \( \varSigma _{i_0} \backslash T_{i_0} \) . Since \(d_{\varGamma } (\cdot , e )\) is 1-Lipschitz, there are no edges between \(Y_0\) and \(Y_{1/2}\) , and by the definition of \(T_{i_0}\) there are no edges between \(Y_{1/4}\) and \(Y_{3/4}\) .

Then construct a map \(\psi : \varGamma \rightarrow \mathbb {R} / \mathbb {Z} \) that restricted to \(Y_s\) equals s for \(s \in \{ 0, 1/4, 1/2, 3/4 \}\) , and takes all edges joining \(Y_0\) with \(Y_{1/4}\) to the interval [0, 1/4], doing the same for the intervals [1/4, 1/2], [1/2, 3/4], and [3/4, 1].

By construction, \(\psi \) sends each edge of \(\varGamma \) to either a point or an interval of length 1/4 in \( \mathbb {R} / \mathbb {Z} \) . Also recall that each 2-cell \(\alpha \) of \(P_3(\varGamma )\) is attached to \(\varGamma \) via a simple loop \(\partial \alpha \) of length \(\le 3\) . Therefore, \(\psi (\partial \alpha ) \subset \mathbb {R} / \mathbb {Z} \) is a loop of length \(\le 3/4\) hence nullhomotopic for each \(\alpha \) , and \(\psi \) extends to a map \(\varPsi : P_3(\varGamma ) \rightarrow \mathbb {R} / \mathbb {Z} \) (see Fig.  5 ).

figure 5

Each edge of \(\varGamma \) is sent via \(\psi \) to either a point or an interval of length \(\le 1/4\) , so \(\psi \) extends to a map \(\varPsi : P_3(\varGamma ) \rightarrow \mathbb {R}/\mathbb {Z}\)

Assume the claim is false and take a minimizing path \([ e=g^{\prime }_0,g^{\prime }_1, \ldots , g^{\prime }_{m^{\prime }}=h ] \) in \(\varGamma \backslash T_{i_0} \) . Consider the map \(\varPhi : \mathbb {R}/\mathbb {Z} \rightarrow P_3 (\varGamma )\) that sends the interval [0, 1/2] to the path \([g_0,g_1, \ldots ,g_m]\) and [1/2, 1] to the path \([g^{\prime }_{m^{\prime }}, \ldots , g^{\prime }_1, g^{\prime }_0]\) .

Since \(\varPsi \circ \varPhi (0) = 0\) , \(\varPsi \circ \varPhi (1/2) = 1/2\) , \(\varPsi \circ \varPhi \vert _{[0, 1/2]}\) misses 3/4, and \(\varPsi \circ \varPhi \vert _{[1/2, 1]} \) misses 1/4, the composition \(\varPsi \circ \varPhi \) is homotopic to the identity in \( \mathbb {R} / \mathbb {Z} \) , meaning that the induced map \(\varPsi _{*}: \pi _1(P_3(\varGamma )) \rightarrow \pi _1( \mathbb {R} / \mathbb {Z} )= \mathbb {Z}\) is surjective, contradicting the hypothesis \({\text {b}_1}(P_3(\varGamma )) =0\) . This finishes the proof of the claim.

Claim 2: For each \(i_0 \in \{ 1, \ldots , m-1 \}\) , either

\(g_{i_0}^{-1}T_{i_0}\) or \(hg_{i_0}^{-1}T_{i_0}\) intersect \(T_{i_0}\) .

Let \(C_1, \ldots , C_{\ell } \subset \varGamma \) denote the connected components of \(\varGamma \backslash T_{i_0}\) , with \(e \in C_1\) , \(h \in C_2\) . Observe that \(g_{i_0}^{-1}C_1, \ldots , g_{i_0}^{-1}C_{\ell }\) are the connected components of \(\varGamma \backslash g_{i_0}^{-1}T_{i_0}\) , and \(hg_{i_0}^{-1}C_1, \ldots , \) \(hg_{i_0}^{-1}C_{\ell }\) are the connected components of \(\varGamma \backslash hg_{i_0}^{-1}T_{i_0}\) .

Assume \(T_{i_0} \cap g_{i_0}^{-1}T_{i_0} = \emptyset \) . Since \(g_{i_0}^{-1}T_{i_0}\) is connected and contains e , it is contained in \( C_1 \) . By Lemma  35 , \(\varGamma \backslash C_1 = T _{i_0}\cup C_2 \cup \ldots \cup C_{\ell }\) is connected, and since it doesn’t intersect \(g_{i_0}^{-1}T_{i_0}\) , it is contained in \(g_{i_0}^{-1}C_{j_1}\) for some \(j_1\) . Therefore

This is only possible if \(j_1 = 1\) , and in particular we have

Similarly, if \(T_{i_0} \cap hg_{i_0}^{-1}T_{i_0} = \emptyset \) , then \(hg_{i_0}^{-1}T_{i_0}\) is contained in \(C_2\) . By Lemma 35 , \(\varGamma \backslash C_2 = T_{i_0} \cup C_1 \cup C_3 \cup \ldots \cup C_{\ell }\) is connected, and since it doesn’t intersect \(hg_{i_0}^{-1}T_{i_0}\) , it is contained in \(h g_{i_0}^{-1}C_{j_2}\) for some \(j_2\) , meaning that

This implies that \(j_2 = 2\) and

Assuming the claim is false, both ( 19 ) and ( 20 ) would hold; a contradiction.

From the second claim, we deduce \(\text {diam} (T_i) \ge \min \{ i, m-i \}\) for each \(i \in \{ 1, \ldots , m -1 \}\) , and since the \(T_i\) ’s are disjoint, we conclude that

This implies that \(m \le \sqrt{4\vert G \vert +1} -2\) , which is the required inequality. \(\square \)

Let \(p \in X\) and define S as in Proposition  4 with \(\delta = 0 \) . By Proposition  5 , the first Betti number of \(P_3(\varGamma (G, S))\) vanishes. For \(x, y \in X\) , take \(g_1, g_2 \in G \) with \(d_X(g_1 p, x), d_X(g_2 p, y ) \le {\text {diam}}(X/G)\) . Then

where the second inequality follows from Švarc–Milnor Lemma and the third one from Theorem  6 . The result follows since \(\sqrt{4 \vert G \vert + 1} \le 2 \sqrt{\vert G \vert } + 1\) . \(\square \)

Pick \(p_n \in X_n\) , set \(S_n: = \{ g \in G_n \vert d(gp_n, p_n) \le 2 \cdot {\text {diam}}(X_n / G_n ) \} \) , and let \(\varGamma _n: = \varGamma (G_n, S_n)\) . If the result fails, there is \(\varepsilon > 0\) such that after taking a subsequence one has

By the Švarc–Milnor Lemma, this would imply \( \vert G_n \vert ^{\varepsilon } = O \left( {\text {diam}}(\varGamma _n ) \right) . \) Then by [ 5 , Theorem 1], after further taking a subsequence, \(\varGamma _n / {\text {diam}}(\varGamma _n)\) converges to an m -dimensional torus X . By Remark  27 , the sequence \(P_3(\varGamma _n) / {\text {diam}}(P_3(\varGamma _n))\) also converges to X and by [ 34 , Theorem 2.1] there are surjective morphisms \(\pi _1 (P_3(\varGamma _n)) \rightarrow \pi _1 (X) = \mathbb {Z}^m\) for large enough n , contradicting Proposition  5 . \(\square \)

5 Fourier analysis in abelian groups

In this section we prove Theorem  9 and Corollaries  10 and  11 . Let k , G , S be as in the statement of Theorem  9 and let \(\varGamma : = \varGamma (G,S) \) . Assuming the estimate ( 3 ) fails to hold, there is an irreducible non-trivial unitary representation \(\rho : G \rightarrow U(m)\) and \(x \in \mathbb {S}^{2\,m-1}\) with

By Proposition  32 we have \(m = 1\) , and since the metric on \(\mathbb {S}^1 \) is bi-invariant, we can assume \( x = 1\) . Let \(\psi : \varGamma \rightarrow \mathbb {S}^{1}\) be the map that restricted to G coincides with \(\rho \) , and restricted to an edge \([g,h] \subset \varGamma \) is a minimizing geodesic from \(\rho (g)\) to \(\rho (h)\) .

If \(g,h \in G\) are such that \(g = hs\) for some \(s \in S\) , then ( 21 ) implies that the angle between \(\rho (g) \) and \(\rho (h)\) is less than \(2 \pi / k \) . Hence, for any simple loop of length \(\le k\) in \(\varGamma \) , its image under \(\psi \) has length less than \(2 \pi \) and is contractible. Therefore, \(\psi \) extends to a map \(\varPsi : P_k (\varGamma ) \rightarrow \mathbb {S}^1\) .

Since \(\rho \) is non-trivial, there is \(s \in S\) with \(\rho (s) \ne 1\) . Then the image under \(\varPsi \) of the loop \([ e, s, s^2, \ldots , s^{\vert G \vert } =e]\) is a loop in \(\mathbb {S}^1\) that winds around at least once; counterclockwise if \({\text {Re}}(\rho (s))>0\) and clockwise if \({\text {Re}}(\rho (s) ) < 0\) . This means the map \( \varPsi _{*}:\pi _1 (P_k (\varGamma ) ) \rightarrow \pi _1(\mathbb {S}^1) = \mathbb {Z}\) is non-trivial, contradicting the assumption \({\text {b}_1}(P_k(\varGamma )) = 0\) . This finishes the proof of ( 3 ).

We now proceed to prove ( 4 ). Notice that if we simply apply ( 2 ) naively to ( 3 ) we would get a weaker result. Let \( - \lambda \in \sigma (\varDelta )\backslash \{ 0 \} \) , and \(E_{\lambda } \le \mathbb {C} [G]\) the corresponding eigenspace. By Lemma  31 , there is \(x \in E_{\lambda } \) with \(\vert x \vert = 1\) such that the span of its orbit is an irreducible representation \(\rho : G \rightarrow \mathbb {S}^1\) . Since \(\lambda \ne 0\) , it follows that \(\rho \) is non-trivial.

Case 1 \(\rho (s) \ne -1\) for all \(s \in S\) .

By ( 3 ), there is \(t \in S\) with \(d(\rho (t), 1) \ge 2 \cdot \sin (\pi / k)\) . This implies \({\text {Re}}(\rho (t) ) = {\text {Re}}(\rho (t^{-1})) \le \cos ( 2 \pi / k )\) . Since \(\rho (t) \ne -1\) , one has \(t \ne t^{-1}\) so

where in the last line we used that \({\text {Re}}(\rho (s)) < 1\) for all \(s \in S \backslash \{ t, t^{-1} \} \) .

Case 2 \(k = 3 \) and \(\rho (t) = -1\) for some \(t \in S\) .

We claim there are \(s_1, s_2 \in S \backslash \{ e, t \}\) such that \(s_1s_2 = t\) . Assume otherwise; then the edge \([e,t ] \subset \varGamma \) does not belong to a 2-cell of \(P_3(\varGamma )\) . Let x be the midpoint of the edge [ e ,  t ], \(A:= [e,t]\) , and \(B:= P_3(\varGamma ) \backslash \{ x \}\) . Then \(A \cap B = [e, x) \cup (x, t ]\) and by Lemma  28 , B is connected, so the portion of the Mayer–Vietoris sequence (with real coefficients)

yields the exact sequence (using \({\text {b}_1}(P_3(\varGamma ) = 0)\) )

This is impossible by dimension arguments. Then there are \(s_1, s_2 \in S \backslash \{ e, t \}\) (not necessarily distinct) with \( s_1 s_2= t\) . Since \(\rho (s_1)\rho (s_2) = -1\) , without loss of generality we can assume \({\text {Re}}(\rho (s_1)) \le 0 \) . Then

Case 3 \(k \ge 4\) and \(\rho (t) = -1\) for some \(t \in S\) .

Directly compute

This, together with ( 2 ), finishes the proof of ( 4 ).

For notational convenience, we set

To prove ( 5 ), we look at the random walk \(W_{\alpha _k}^t\) in \(\varGamma \) .

For any non-trivial irreducible unitary representation \(\rho : G \rightarrow \mathbb {S}^1\) ,

This is a direct computation using ( 11 ). On one hand we have

where we first used the identity \({\hat{\delta }}_s (\rho ) = \rho (s)\) and then the estimate \(\lambda _1 \ge 2 \xi _k\) . For the other inequality, notice that \(\alpha _k - 2 \vert S \vert = 2 \xi _k - \alpha _k\) , then

where we used \({\text {Re}}(\rho (s)) \ge -1 \) for all \(s \in S\) in the inequality. \(\square \)

Then by ( 15 ), for \(t \in \mathbb {N}\) we have

where we used ( 8 ) for the inequality. Now assume \(t \le {\text {diam}}(\varGamma )\) . Since \(W^t_{\alpha _k}\) is supported in the ball of radius t around e , then the left hand side of the equation is at least \( \frac{1}{\vert G \vert ^3}\) . Hence by taking logarithm and using the identity \(\log (1 + u ) \le u\) we get

Rearranging terms,

This implies

This concludes the proof of Theorem  9 . Notice that if \(k = 3\) , then ( 5 ) simplifies to

In order to prove Corollary  10 , we need to establish an analogue of Lemma  36 .

Under the hypothesis of Corollary  10 , for any non-trivial irreducible unitary representation \(\rho : G \rightarrow \mathbb {S}^1\) one has

This is again a direct computation. Using \(\lambda _ 1 \ge 2 \xi _k\) we get

On the other hand, simply using \({\text {Re}}(\rho (s)) \ge -1\) for all \(s \in S\) we conclude

Corollary 10

By ( 16 ), using Lemma  37 and ( 8 ), we have

for \(t \in \mathbb {N}\) . If \(\varepsilon (t) \ge c \in [0, 2] \) , then taking logarithms as above we get

Rearranging terms we get

Since \(\xi _k \ge 16/k^2\) the result follows. \(\square \)

Corollary 11

Take a point \(p \in M \) with injectivity radius \(\ge 2r_0\) , \({\tilde{p}} \in {\tilde{M}}\) in its preimage, and set

By the injectivity radius condition, for \(g,h \in \pi _1(M)\) distinct, the balls \(B(g{\tilde{p}}, r_0)\) and \(B(h{\tilde{p}}, r_0)\) are isometric and disjoint. Since \(g \in S \cup \{ e \}\) implies \(B(g{\tilde{p}}, r_0) \subset B({\tilde{p}}, 2D + r_0)\) , we have

By the Bishop–Gromov inequality [ 6 , Section 11.10], the right hand side of the equation is less or equal than \(v _{n}^{\kappa } (2D + r_0) / v_n^{\kappa }(r_0)\) . By Proposition  5 , \(P_3(\varGamma (\pi _1(M), S))\) is simply connected, so ( 22 ) holds;

Arguing as in the proof of Theorem  2 , we have

Combining ( 23 ) and ( 24 ) the result follows. \(\square \)

Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The author would like to express his thanks to Cameron Rudd and Andrew Ng for suggesting Example  18 , and Jacob Bradd, Ana C. Chávez-Cáliz, and Anton Petrunin for lengthy discussions and helpful comments about previous versions of this paper. He is also grateful to Sebastian Gouzel for pointing out the ideas in [ 10 , 11 , 13 , 28 ] to him, stimulating his interest in Theorem  9 even further, and an anonymous reviewer whose contributions have significantly improved not only the presentation of this paper but the quality of the results. Starting from Summer 2022, the author holds a Postdoctoral Fellowship at the Max Planck Institute for Mathematics at Bonn.

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Zamora, S. Fundamental groups and group presentations with bounded relator lengths. Geom Dedicata 218 , 80 (2024). https://doi.org/10.1007/s10711-024-00915-1

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DOI : https://doi.org/10.1007/s10711-024-00915-1

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AI + Machine Learning , Announcements , Azure AI Content Safety , Azure AI Studio , Azure OpenAI Service , Partners

Introducing GPT-4o: OpenAI’s new flagship multimodal model now in preview on Azure

By Eric Boyd Corporate Vice President, Azure AI Platform, Microsoft

Posted on May 13, 2024 2 min read

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Microsoft is thrilled to announce the launch of GPT-4o, OpenAI’s new flagship model on Azure AI. This groundbreaking multimodal model integrates text, vision, and audio capabilities, setting a new standard for generative and conversational AI experiences. GPT-4o is available now in Azure OpenAI Service, to try in preview , with support for text and image.

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A step forward in generative AI for Azure OpenAI Service

GPT-4o offers a shift in how AI models interact with multimodal inputs. By seamlessly combining text, images, and audio, GPT-4o provides a richer, more engaging user experience.

Launch highlights: Immediate access and what you can expect

Azure OpenAI Service customers can explore GPT-4o’s extensive capabilities through a preview playground in Azure OpenAI Studio starting today in two regions in the US. This initial release focuses on text and vision inputs to provide a glimpse into the model’s potential, paving the way for further capabilities like audio and video.

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  • Enhanced customer service : By integrating diverse data inputs, GPT-4o enables more dynamic and comprehensive customer support interactions.
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  • Content innovation : Use GPT-4o’s generative capabilities to create engaging and diverse content formats, catering to a broad range of consumer preferences.

Exciting future developments: GPT-4o at Microsoft Build 2024 

We are eager to share more about GPT-4o and other Azure AI updates at Microsoft Build 2024 , to help developers further unlock the power of generative AI.

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    We study the geometry of compact geodesic spaces with trivial first Betti number admitting large finite groups of isometries. We show that if a finite group G acts by isometries on a compact geodesic space X whose first Betti number vanishes, then \({\text {diam}}(X) / {\text {diam}}(X / G ) \le 4 \sqrt{ \vert G \vert }\).For a group G and a finite symmetric generating set S, \(P_k(\varGamma ...

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