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− | In this talk I will describe the Church-Ellenberg-Farb philosophy of counting points on varieties over finite fields. I will talk about some connections between homological stability and | + | In this talk I will describe the Church-Ellenberg-Farb philosophy of counting points on varieties over finite fields. I will talk about some connections between homological stability and asymptotics of point-counts. Time permitting, we will see how this fits into the framework of FI-modules. |
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Revision as of 21:25, 24 February 2019
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]\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]GL_n(\mathbb{F}_q)[/math] |
I will discuss the irreducible representations of [math]GL_n(\mathbb{F}_q)[/math]. In particular, I will discuss some ways in which we can understand the structure of representations of [math]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]\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. |
Feb 19
Qiao He |
L-functions, Heegner Points and Euler Systems |
This talk will be about the L-function of an elliptic curve. I will introduce the Gross-Zagier and the Waldspurger formulae, and try to explain why they are deep and useful for the study of L-functions of elliptic curves. |
Feb 26
Soumya Sankar |
Representation stability and counting points on varieties |
In this talk I will describe the Church-Ellenberg-Farb philosophy of counting points on varieties over finite fields. I will talk about some connections between homological stability and asymptotics of point-counts. Time permitting, we will see how this fits into the framework of FI-modules. |