Student Number Theory Seminar
Date
Speaker
Title and Abstract
February 14
February 28
Title: Number theory courses and a brief introduction to the circle method.
Abstract: We will discuss our department's graduate course offerings in number theory. Afterward, we will briefly discuss the circle method, which uses detector functions coming from analysis to count integer solutions to equations and inequalities.
March 20
Title: Math 997 Fall 2024.
Abstract: I will give an overview for Math 997. The theme for the Fall semester will be random models in number theory. The main goal is to explore statistics of L-functions and multiplicative functions (e.g. Mobius function) through good random models .
April 17
Maitreyo Bhattacharjee
https://sites.google.com/view/maitreyo-bhattacharjee
Zoom Recording of the talk:
Title: When Number Theory meets Random Matrix Theory.
Abstract: The theory of random matrices has many surprising and diverse applications to problems emerging in number theory. In this talk, we will focus on how RMT heuristics can be used to model value distributions of the zeta function on the critical line, leading us to conjecture the main terms of its integral moments. The talk will be accessible to students having a background in Elementary Number Theory, and no prior exposure to random matrix theory will be assumed.
May 1
Shubham Nikam
Title: A brief introduction to Modular Forms.
Abstract: In this talk, I will introduce modular forms and Eisenstein series. I will briefly discuss cusp forms and their relation to the Fourier series expansion of Eisenstein series. Specifically we will see how the Fourier coefficients relate to the Ramanujan Tau function. Time permitting, I will present a few results including the dimensions of spaces of modular forms of different weights.