Title: L-Functions and Murmurations
Abstract: In this talk, I will start with the famous Riemann zeta function and its basic properties, as well as how it helps us study prime numbers. Next I will give a brief introduction to L-functions, which generalize the Riemann zeta and is ubiquitous in number theory - for examples I will describe L-functions associated to Dirichlet characters, number fields, elliptic curves, modular forms, and Galois representations. Then I will discuss some statistical aspects of the study of L-functions. Time permitting, I will talk about murmurations - a new oscillatory pattern in the coefficients of families of L-functions that is recently discovered by machine learning scientists - and maybe a murmuration function that I computed for my undergraduate thesis.
Note: The talk will start at 4:10 pm