Upcoming Talks

Feb. 5

• Speaker: Max Weinreich
• Title: How to play billiards like a mathematician
• Abstract:  The theory of mathematical billiards describes how a laser beam reflects in a mirror. In this talk, we’ll see how to explain some amazing pictures that come from firing a laser inside an ellipse. Along the way, we will learn about the beautiful mathematics of geodesic flow, which ties together many of the great things in life: bowling, space travel, pancakes, coffee, and algebraic geometry.

Feb. 19

• Speaker: Gage Martin
• Title: The Birman-Hilden Correspondence
• Abstract:  Braids are a useful tool 3-dimensional topologists use in the study of knots and links. Meanwhile the mapping class group of a surface is an active area of research in 2-dimensions. In this talk we introduce both these concepts and see a beautiful connection between them due to Birman-Hilden. If time permits we may discuss applications of the theory and contemporary open questions.

Mar. 5

• Speaker: Andy Senger
• Title: Scissors congruence: classical results and modern perspectives
• Abstract:  Two polytopes P and Q are said to be scissors congruent if you can cut P into finitely many polytopes that can be rearranged to fit back together into Q. How can we determine when two polytopes are scissors congruent? I’ll discuss classical results in dimensions 2 and 3, including the solution to Hilbert’s third problem, and then attempt to describe modern connections between this problem and topics such as group homology, motives, and algebraic K-theory.

Mar. 26

• Speaker: Eli Grigsby (Boston College)
• Title: Neural networks and the geometry and topology of decision problems
• Abstract:  Deep neural networks can drive cars, produce images from text prompts, and write titles and abstracts for undergraduate math lectures (J/K…or am I?). I’ll begin by explaining what a neural network is as a mathematical object, describe the geometry behind how they approach decision problems (e.g., is this e-mail spam: Yes or no?), and then describe a beautiful and under-advertised construction due to Marissa Masden of Oregon: the computation of the homology groups of the geometric decision regions and boundaries of a deep neural network from an elementary, combinatorially-defined cubical complex.

Apr. 9

• Speaker: Kevin Yang
• Title: Singular stochastic partial differential equations
• Abstract:  A singular SPDE is a PDE that contains random terms, but which cannot be solved (in any reasonable sense) using purely analytic ideas. Nevertheless, the goal of trying to make sense of these equations is motivated by the fact that their stories are often surprising. We will discuss one such story, which happens to relate (conjecturally) a game of sticky Tetris, burning paper, and the longest increasing subsequence of a random permutation.

Apr. 23

• Speaker: Alex Kapiamba
• Title: Dynamics, fractals, and the Mandelbrot set
• Abstract:  A fundamental goal in mathematics is to describe the behavior of systems that change over time. While these dynamical systems are everywhere, most are far too complicated to give a complete description. In this talk we will explore how even some of the simplest dynamical systems give rise to rich behavior, and how this behavior can be understood via fractal geometry.