NTSGrad Spring 2019/Abstracts
This page contains the titles and abstracts for talks scheduled in the Spring 2019 semester. To go back to the main GNTS page, click here.
Jan 29
Ewan Dalby |
Approximating the mean square of the product of the Riemann zeta function with Dirichlet polynomials |
Understanding the asymptotics of the mean square of the product of the Riemann zeta function with Dirichlet polynomials allows one to understand the distribution of values of L-functions. I will introduce the problem and describe several results from the paper of Bettin, Chandee and Radziwill who showed how to pass the so called [math]\displaystyle{ \theta=1/2 }[/math] barrier for arbitrary Dirichlet polynomials. This will be a prep talk for Thursdays seminar. |
Feb 5
Sun Woo Park |
Representations of [math]\displaystyle{ GL_n(\mathbb{F}_q) }[/math] |
I will discuss the irreducible representations of [math]\displaystyle{ GL_n(\mathbb{F}_q) }[/math]. In particular, I will discuss some ways in which we can understand the structure of representations of [math]\displaystyle{ GL_n(\mathbb{F}_q) }[/math] , such as parabolic inductions, Hopf algebra structure, and tensor ranks of representations. This is a preparatory talk for the upcoming talk on Thursday. |
Feb 12
Hyun Jong Kim |
The integrality of the j-invariant on CM points |
The j-function, a complex valued function whose inputs are elliptic curves over [math]\displaystyle{ \mathbb{C} }[/math], classifies the isomorphism class of such elliptic curves. We show that, on elliptic curves with complex multiplication (CM), the j-function takes values which are algebraic integers. |