##### Department of Mathematics,

University of California San Diego

****************************

### Graduate Student Colloquium (Math 296)

## Aaron Pollack

#### UCSD

## Harmonic theta functions

##### Abstract:

A modular form is a certain holomorphic function on the complex upper half plane which has an infinite group of discrete symmetries. I will discuss modular forms and some of their generalizations. In particular, I will try to answer the following questions: What is a modular form? What are some examples of modular forms? What is a simple open question about modular forms? The examples of modular forms I will give go under the name of "harmonic theta functions". Time permitting, I will describe some exotic variants of these harmonic theta functions that are tied up with the octonions and the compact Lie group G_2.

Host: Jonathan Novak

### February 1, 2023

### 4:00 PM

APM 7321

****************************