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 |
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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] |
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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 |
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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. |
Feb 19
| Qiao He |
| L-functions, Heegner Points and Euler Systems |
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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 |
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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 its connection to asymptotics of point-counts. Time permitting, we will see how this fits into the framework of FI-modules. |