Lectures

We invite various University of Texas at Austin faculty members to join us and give lectures about their research, with occasional lectures on other topics. As such, members get the chance to learn about many different subjects in mathematics from a variety of perspectives.

## Upcoming:

### Dr. Aaronson: Hao Huang's Proof of the Sensitivity Conjecture and Its Implications

###### November 20th, 2020 at 17:00 CDT

On Zoom, Dr. Aaronson will be giving a lecture on Hao Huang's Proof of the Sensitivity Conjecture and Its Implications. This is a recent result in combinatorics and theoretical computer science. Scott Aaronson is a theoretical computer scientist and David J. Bruton Centennial Professor of Computer Science at The University of Texas at Austin, and director of its Quantum Information Center. He taught for nine years in Electrical Engineering and Computer Science at MIT. His research interests center around the capabilities and limits of quantum computers, and computational complexity theory.

## Past:

### Hunter Vallejos: Ergodicity of Billiard Flow and Translation Surfaces

###### September 7th, 2020 at 17:00 CDT

Physics, Math, and Astronomy Building Room 5.126

After an elementary physics motivation, we will think about the dynamics of a ball on a billiard (pool) table. It turns out that one can “unfold” a billiard table to get what is called a translation surface; using this, we can rephrase the question of dynamics of a ball on a billiard table into a question about the dynamics on a “moduli space” of translation surfaces. We will finish with a statement of a theorem of Kerkhoff, Masur, and Smillie: in 1986, they proved that billiard flow is uniquely ergodic in almost every direction. This is an introductory talk to a particular field of research in mathematics.

###### September 21st, 2020 at 17:00 CDT

Physics, Math, and Astronomy Building Room 5.126

Jacky Chong is a post-doc researcher at the University of Texas at Austin. His research “lies in the intersection of partial differential equations and quantum many-body physics”. He will give a brief tour on some of the ongoing mathematical research in the field of (quantum) many-particle systems. The talk will mainly focus on ideas rather than mathematics. The goal of the talk is to expose the audience to some of the exciting developments of large quantum systems.

### Jacky Chong: "Mean-Field Dynamics: From Microscopic to Macroscopic

### Charles Reid: What can you hear about the shape of a drum?

###### September 7th, 2020 at 17:00 CDT

Physics, Math, and Astronomy Building Room 5.126

Differently shaped drums often sound different, for example a circular drum sounds different from a square drum, but can you tell the exact shape of a drum just by listening to it? In a 1966 article titled "Can one hear the shape of a drum" Mark Kac popularized a mathematical version of this question: Is a plane region determined by the spectrum of it's laplacian? It turns out that the answer is no, but counterexamples weren't found until 1992. I will mention the counterexamples, but I will focus on the things you can hear about a drum. Thinking about the heat equation will allow us to "hear" the area, the perimeter, and something about the angles of the drum. The wave equation on the other hand will let us hear something more mysterious: lengths of closed paths a ball could take if you made the drum into a frictionless pool table (aka closed billiard trajectories). Kac's question may seem whimsical, but it leads to some of the deepest connections in math.