Acknowledgments: Special THANKS to Matthias Beck, Ben Braun, Pamela Harris, Max Hlavacek, Mariel Supina, Julie Vega, and the Discrete Geometry Group/The Villa at FU Berlin.
I recently came back from a research visit to the Freie Universität in Berlin where I was visiting Professor Matthias Beck and the Discrete Geometry group there. I was invited to give a talk in their seminar and was also invited to give a talk in the Discrete and Convex Geometry Seminar at the Technische Universität. I want to take the time to reflect on giving talks and to think about things related to preparing and presenting talks. Note that these are just my thoughts and reflections; the things mentioned here may not apply to everyone or may not be the best approaches for different kinds of talks.
I have been in the audience for many talks in my time as a student. I have experienced some wonderful talks, a few more okay talks, and unfortunately a larger number of not-so-good talks. I believe that part of doing mathematics is also communicating it effectively (whatever that may mean). I was fortunate that during my time at the Freie Universität, Prof. Beck, graduate students, and post-docs started a “soft skills” seminar, and one of the seminar topics was on how to give a good talk. In the seminar we shared things that stood out to us at talks that we have sat through in the past. Some of these things were good and constructive, but many found “bad talks” more memorable. I’d venture to say that giving talks is quite challenging and is always an area where we can improve in.
Compiling some feedback I received about my talk and modifications/explanations from advice given in (, , , ), here is a list and some thoughts on things to do for a talk:
- Only give talks if you want to (or “have” to)
- If you don’t have the desire to speak then you might have a negative attitude towards giving a talk and it will most likely lead to one of these “bad talks”
- If you “have to” present a talk (e.g., master’s defense, PhD defense, course requirement, etc.), know that life continues beyond these things. Believe in yourself, you got this.
- PLAN, PLAN, PLAN, PREPARE, PREPARE, PREPARE
- I think most of the times I have felt that my talks have not gone well is partly due to my lack of preparation.
- You might feel better going into a talk if you feel prepared.
- When preparing your talks keep in mind that they may look different if you are giving a seminar talk, colloquium, expository talk, research-focused talk, board talk, slide talk, etc.
- Give a talk more than once, it will get better and better.
- Some people understand their own research better after preparing/giving a talk; this and potential feedback may help in writing up results.
- Know who your audience is and where you are talking
- In preparing your talk, it is important to know who you are speaking to in order to prepare a talk that is an appropriate level.
- Will you be giving a board talk or slide talk? Does the room have boards accessible even if you are giving a slide talk?
- Be mindful of your audience/Aim to be inclusive
- This can be interpreted in many ways and can be adapted at different moments.
- An example that comes to mind is when using colored chalk or markers; I had an audience member at a talk who had difficulty seeing (or could not see) a certain color on the board, I quickly changed colors.
- If a microphone is provided, please always use it. You never know who may have difficulties hearing.
- Thank your audience and the organizers of the seminar/conference and people that invited you. It is always nice to hear speakers are happy to be speaking with the audience.
- Another thing is not assume the gender or other identities of your audience.
- Do not overestimate the knowledge of your audience
- When I gave my seminar talk, one of the audience members thanked me afterwards for defining a certain geometric object. My research is in geometric combinatorics, hers was in algebraic topology; while she uses tools from discrete geometry, not all the objects were common knowledge in her field.
- Tell a Story: Context, Motivation, Applications, and the Future
- Your project/research tells a story. It is useful to keep that in mind and prepare your presentation as a guide to tell a story.
- What is the context of your talks? What is the aim of the project?
- Share how you became interested in the topic.
- Share how your work has applications to other fields of mathematics, society, science, etc.
- Share open problems or conjectures. This might get people invested in your work and you may find new collaborators!
- Every story has an ending. Aim to have a nice finish. This may include some of things mentioned above.
- Examples and Intuitive Definitions
- Use helpful examples to illustrate definitions, special cases, or even proof ideas.
- Avoid technical definitions, this will more than likely lead to confusion. This happened during one of my talks; the definition was long and could been expressed more straightforward with an example.
- Try to have a unifying or guiding example. This is may be helpful and more friendly to the audience.
- Repeatedly remind the audience of unfamiliar definitions.
- PICTURES ARE YOUR FRIENDS!
- Use colors to highlight or underline key points.
- Use computations if they are illustrative of a main point.
- Realize that people in your audience who are interested in details can look at your papers/preprints. Examples > Technical Proofs
- Board Work and Punctuation/Symbols Matter
- Try to write as neat as possible. For me, I typically write in cursive and so I try to write in print to have it be legible for others. Also, I try really hard to write as slow/effectively so that my writing does not tilt as I write across the board.
- Punctuation and symbols matter. There is a popular example of where commas are important: “Let’s eat grandma” and “Let’s eat, grandma.”
- Something similar arose during one of my talks. I hyphenated a mathematical term and that led to confusion because it has different meanings when you hyphenate. Be careful.
- Questions and how to handle them
- Anticipate questions you may be asked.
- Encourage questions, this keeps people engaged and you can gauge whether people are following your talk.
- If there is a time constraint, you can also ask that people save their questions to the end.
- You might have an audience that does not have any questions during the talk, that is okay. You may want to ask the audience questions in return.
- When asked a question, acknowledge the person asking the question by walking in their direction and repeat the question for the rest of the audience who might have missed it.
- You might have an audience that actively (or excessively) asks questions. This shows interest, so don’t be deterred. At times this can be a bit challenging when questions are asked during talks. Feel free to answer them or save them for after the talk. You are in charge.
- Find a way to comfortably say “I don’t know the answer to your question.” Prof. Beck likes something along the lines of, “this is an interesting question, and I’d be happy to explore it—I don’t think I know the answer”.
- Feel free to ask an organizer to let you know or give you a sign when you have a certain amount of time left.
- Know where the clock in the room is or have a watch.
- Try not to exceed your allotted time. If you exceed your time it shows that you may have been unprepared. Also, people might have to be somewhere right after your talk. Let’s aim to respect people’s time.
- Give credit where credit is due
- Thank your co-authors/collaborators.
- Give references to other people’s work.
- Cite theorems, authors, and the year of the result. Mention references if possible. This also helps others seek out the relevant works if they are interested and it helps people put your work into context
- Give yourself credit. Tell people what work is yours! You’ve done great research, why not tell people it’s yours?
- BE YOUR AUTHENTIC SELF
- Only YOU really know what this truly means!
- Don’t belittle your own work/results or downplay your knowledge. You are an expert! (this is something I struggle with all the time)
- Personalize your presentation. For some people this looks like showing humor, pictures, quotes, anecdotes, etc.
- Wear clothes and shoes you are comfortable with.
- Show enthusiasm for your work, in your own special way.
- People will reciprocate your energy.
- You are a rock star!
Further Reading – Other Resources for Presentations: Handouts and Links
 Devadoss, Satyan L. “Planning Ahead for the Joint Meetings: Giving Good Talks.” Notices of the AMS, Vol. 66, no. 10, pp. 1647-1651.
 Gallian, Joseph A. “Advice on Giving a Good PowerPoint Presentation.” Math Horizons, vol. 13, no. 4, 2006, pp. 25–27.
 Kyra, Bryna. “Giving a Talk.” Notices of the AMS. Vol. 60, no. 2, pp. 242-244.
 McCarthy, John E. “How to Give a Good Colloquium” Canadian Mathematical Society NOTES, Vol. 31, no. 5, pp. 3-4.
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