# Seminar

This seminar is intended for an undergraduate audience. If you have an interesting talk that would be suitable for undergrads, feel free to contact the organizers and volunteer as a speaker. We especially appreciate talks by undergrads for undergrads!

A large part of mathematical culture happens in seminars, where ideas are discussed informally and with a healthy dose of friendly laughter. There are no grades, evaluations, or judgement. Before the COVID-19 Pandemic, we had pizza!

Seminar runs Wednesdays 14-15:00 (EST) on Zoom. We start seminar at 14:05, to let people arrive and get settled.

After attending seminar, we ask that participants fill out this feedback form. If you are not able to use Google Forms and would still like to give feedback, please e-mail the organizers.

The *prime factorization* of the Meeting ID is: $11 \times 59 \times
124877917$. The passcode for the meeting is: seminar. If you have trouble
accessing the seminar, please contact the co-organizers: Parker Glynn-Adey and
Lisa Jeffery. We will send you a direct
link.

At the bottom of this page, there FAQ for speakers.

Date | Speaker | Title | Notes |
---|---|---|---|

May 26 | Brian Li | Cops and Robbers with Many Variants | video / slides |

June 2 | Parker Glynn-Adey | The Probabilistic Method | video / slides |

June 9 | Ben Chislett | Ray Tracing and the Light Transport Equation | video / slides |

June 16 | Jesse Maltese | An Introduction to Mathematical Logic | video / slides |

June 23 | David Schrittesser | Your life will be better with infinitesimals | |

June 30 | Kevin Santos | An Introduction to Group Theory through Puzzles |

We are listed on ResearchSeminars.org as UndergraduateSeminar.

## Speakers

### June 30: Kevin Santos: An Introduction to Group Theory through Puzzles

*Abstract*:

The concept of a group is a powerful tool that we can use to understand the structures of mathematical objects. In this talk, we’ll use well-known puzzles such as Peg Solitaire, the 15 puzzle, and Rubik’s cube to motivate a brief introduction to the concepts of group theory. We’ll explore how groups are related to symmetry and give some examples of groups, such as the Klein 4-group and the permutation groups. We’ll then see how these ideas can be applied to understand the puzzles.

### June 23: David Schrittesser: Your life will be better with infinitesimals

*Abstract*:
When Leibniz, Newton, and others first developed calculus, they used the
metaphor of infinitely small, or infinitesimal, quantities to try to justify
their methods. Later, infinitesimals were expelled from mathematics and
calculus was made rigorous using the familiar notions of limit and
epsilon-delta formulations.

But infinitesimals have been making a come back! Using methods from logic, in particular model theory, they have been restored as respected citizens in rigorous mathematical arguments. This approach, called non-standard analysis has been described as ``the analysis of the future’'. And indeed, it sometimes allows us to do miraculous things. A recent case in point is my joint result with D. Roy and H. Duanmu, with which we solve a long-standing open problem in statistics (namely giving a Bayesian interpretation of admissibility).

In this talk I will give an introduction to the non-standard method and describe some applications. (And if I manage to spark your interest, come to the course I will teach about this topic at U of T in this fall!)

### June 16: Jesse Maltese: An Introduction to Mathematical Logic

*Abstract*:

In this talk, I will give an introduction to the various ideas underlying the foundations of math. I will first talk through some of the history of the field. Then, I will introduce basic concepts in logic including the definition of truth, a model, and notions like completeness and consistency. Then, I will state two important theorems in the field: Gödel’s Completeness Theorem, and the Compactness Theorem. Finally, I will give some interesting applications of compactness, namely the infinite four-colour theorem and the Ax-Grothendieck Theorem.

### June 9: Ben Chislett: Ray Tracing and the Light Transport Equation

*Abstract*:

Ray Tracing is the primary technique for rendering photorealistic images. Advancements in ray tracing techniques have enabled its use in a variety of computer graphics applications, from animated films to real-time video games. In this talk, we explore the Light Transport Equation, Monte Carlo integration, and some of the many optimizations that have led to ray tracing’s rapid rise in popularity.

### June 2: Parker Glynn-Adey: The Probabilistic Method

*Abstract*:

Mathematicians love purity, intuition, and clarity. We like to construct things explicitly with no messiness. But sometimes, mathematical reality is too weird for our explicit methods. Sometimes, we need to look at random examples to find what we’re looking for. In this talk, we use randomness to produce colourings of complete graphs with no monochromatic cliques, a foundational example of the probabilistic method pioneered by Paul Erdős.

Background in counting and graph theory at the MAT A67 / MAT 202 level will help.

### May 26: Brian Li: Cops and Robbers with Many Variants

*Abstract*:

Mathematics and games complement each other in both mathematical research and learning. Cops and Robbers is a game played on graphs between a set of cops and a single robber. The cops begin the game by moving to a set of vertices, with the robber then choosing a vertex to occupy. All players move from vertex-to-vertex along edges. The cops win by successfully occupying the robber’s vertex, hence catching the robber. We will discuss theorems that help us better understand such games and unleash our creativity to explore many different variants. No prior knowledge required.

## FAQ

- How long should my talk last?
- The longest possible talk is 50 minutes, which allows for five minutes for people to arrive and five minutes for questions. Feel free to use up to 50 minutes. Any talk in the range 15 to 50 minutes would be great.

- Do I need to use a particular format for my slides?
- No, feel free to use any software that you like to make your slides. You don’t even need to make slides. Feel free to draw, or use a whiteboard. For math talks, lots of speakers use Beamer.

- Will my talk be recorded and shared online?
- By default, yes and yes. The talks are recorded to Zoom Cloud and
then Parker edits the recording and puts it on YouTube. If you do
**not**want your talk put online, please let Parker know. He will not post your talk online. We want you to feel comfortable speaking and will accodomate privacy concerns.

- By default, yes and yes. The talks are recorded to Zoom Cloud and
then Parker edits the recording and puts it on YouTube. If you do
- Do I need to present original research?
- No! Feel free to present anything. We especially appreciate introductory talks, which introduce the audience to an novel topic. If you have original research that you would like to present, then please do so in a friendly and introductory manner.

- Do you have any suggestions for things to present?
- Jocelyn R. Bell & Frank Wattenberg (2020) The Slippery Duck Theorem, Mathematics Magazine, 93:2, 91-103, DOI: 10.1080/0025570X.2020.1708693
- Sam Chow, Ayla Gafni & Paul Gafni (2021) Connecting the Dots: Maximal Polygons on a Square Grid, Mathematics Magazine, 94:2, 118-124, DOI: 10.1080/0025570X.2021.1869493