Some tips on math talks: seminar vs. colloquium

One of the requirements for my graduation from the University of Tennessee’s math Ph.D. program is the completion of the presentations seminar. This is a 1-unit course offered by the department designed to train students in the art of giving mathematical talks, and I am taking the course this semester. It seemed like a good time to do so since I passed my oral specialty examination at the end of last semester, and I now have enough original research to revolve a talk around.

While each professor who teaches the course runs it differently, in my case I have three requirements for the course:

1. Give a 40-minute seminar-style talk
2. Give a 40-minute colloquium talk
3. Listen to the other students’ talks and give feedback

At the first course meeting of the semester a few weeks ago, the instructor, Dr. Alex Freire, gave some helpful information and advice for all of us as we prepare our presentations. He highlighted what a seminar-style talk is, what a colloquium talk is, and some of the differences. Since the exposition was so well-organized, I wanted to pass along some of his insights, with my own commentary, as usual.

Picture of me at my oral specialty examination (photo courtesy of Jordan Pellett)

Before proceeding with specifics, I should say that giving talks is an art as much as it is a science. Even if the details of your work are hard, concrete facts, they can be organized and portrayed in many different ways, depending on your audience, how much time you have, and what takeaways you want to leave the audience with.

The seminar talk

Arguably the format with which I’m more familiar with, the idea behind a seminar talk is to present details of your research to a somewhat specialized audience. It seems safe to assume some of the “basics” in your chosen sub-discipline (of course, it’s subjective what can be considered “basic”). With that in mind, here are the general highlights/objectives of a seminar talk:

1. What is the greater context of what you’ve done, and how does it relate to previously established results?
2. Make precise mathematical statements (and concretely showcase data/simulation results you have, if applicable)
3. Provide details of your mathematical proofs, and highlight…