NTSGrad Fall 2019/Abstracts
This page contains the titles and abstracts for talks scheduled in the Fall 2019 semester. To go back to the main GNTS page, click here.
|Law and Orders in Quadratic Imaginary Fields|
To prepare for Thursday's talk, I will give a gentle introduction to the basic theory of complex multiplication for elliptic curves, beginning with a quick review of elliptic curves over the complex numbers.
|The Siegel-Weil Formula|
Theta functions, Eisenstein series, and Adeles, Oh my!
|On The Discrete Fuglede Conjecture|
It's well known that the set of functions from a finite abelian group to the complex numbers forms an inner product space and that any such function can be written as a unique linear combination of characters which are orthogonal with respect to this inner product. We will look specifically at copies of the integers modulo a fixed prime and I will talk about under what conditions can we take a subset of this group, E, and express a function from E to the complex numbers as a linear combination of characters which are orthogonal with respect to the inner product induced on E.
In this talk, I will describe the modularity theorem of elliptic curve. I will state the main theorem first, and then give some consequences of the theorem. If time permitted, I will try to sketch how to construct Galois representation from modular form and describe Langlands-Tunnell theorem, which will be related with Thursday's talk.