Wednesday, November 13, 2019
Time  Items 

All day 

4pm 
11/13/2019  4:15pm Modular forms, which can be seen as functions on $\mathrm{SL}_2(\mathbb{R})/\mathrm{SO}_2(\mathbb{R})$ with certain discrete symmetries, are connected to many areas of both mathematics and physics, and their Fourier coefficients have long been studied for their ability to count various arithmetic objects. After briefly giving an example of this phenomenon I will discuss automorphic forms, which can be seen as their generalizations to groups of any rank. I will give an overview of how to Fourier expand periodic functions on real Lie groups, and of different kinds of Fourier coefficients together with what is known about them. Much is known about Fourier coefficients with respect to maximal unipotent subgroups, but less so for other unipotent subgroups. I will summarize recent work on how to express the latter in terms of the former and when this is possible (e.g. for small automorphic representations of simply laced groups) which is joint work with Gourevitch, Kleinschmidt, Persson and Sahi. I will also briefly describe how this work has applications to string theory where the above Fourier coefficients are interpreted as contributions to graviton scattering amplitudes from nonperturbative effects such as instantons and black holes. Location:
LOM 215

5pm 
11/13/2019  5:00pm Abstract: A graph is a collection of nodes connected by edges. In this talk I’ll present a family of chipfiring games, which start with a placement of chips on the nodes of a graph. After placing the chips, we move them around by “firing” a node, meaning it donates a chip to each of its neighbors. This leads to many mathematical questions: Given two placements of chips, can we move between them using a sequence of chipfiring moves? If so, what’s the fastest way? It not, how can we prove it’s impossible? And if some of the nodes start with a negative number of chips, can we perform chipfiring moves to get those nodes out of debt? This talk will showcase many results and open questions about these chipfiring games, including new theorems proved by undergraduates in Summer 2018. Location:
LOM 206

6pm 
11/13/2019  6:30pm Weekly event for interested students to practice competition math problems in a relaxed setting. Meetings are held every Wednesday from 6:30pm to 8 in LOM 215. All are welcome to attend. Contact Pat Devlin to find out more. Location:
LOM 214/215
