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Texas A&M University
Mathematics

Number Theory Seminar

Fall 2019

 

Date:October 2, 2019
Time:1:45pm
Location:BLOC 220
Speaker:Qibin Shen, University of Rochester
Title:v-adic multiple zeta values over function fields
Abstract:In this talk we will discuss the zero distribution, $\mathbb{F}_q-$, and $\mathbb{F}_q(t)-$ linear relations of interpolated v-adic multiple zeta values over function fields. We will give some combinatorial universal families of algebraic relations hold for multiple zeta values, multiple zeta star values, truncated multiple zeta values, interpolated and motivic v-adic multiple zeta values. We will also introduce our conjecture for the dimension of the linear span of the v-adic multiple zeta values and some interesting behavior of these values.

Date:October 23, 2019
Time:1:45pm
Location:BLOC 220
Speaker:Changningphaabi Namoijam, Texas A&M University
Title:Hyperderivatives of Periods and Logarithms of A Drinfeld Module, and Their Algebraic Relations
Abstract:In 2012, Chang and Papanikolas showed algebraic independence of periods, quasi-periods, certain logarithms and quasi-logarithms of Drinfeld modules. Using Papanikolas’ results on transcendence degree of the period matrix of a t-motive and dimension of its Galois group, we determine algebraic relations among hyperderivatives of periods, quasiperiods, logarithms and quasi-logarithms of Drinfeld modules.

Date:November 13, 2019
Time:1:45pm
Location:BLOC 220
Speaker:Mike Fried, University of California, Irvine
Title:Spaces of sphere covers and Riemann's two types of Θ functions
Abstract:Riemann surface covers XP1z of the sphere, uniformized by a complex variable z, arise by giving the branch points and generators g1gr of a finite group G where the gis have product-one.

By taking any one such cover, and dragging it by its branch points you create a space of such covers.

A Fundamental Problem: For a given G and the conjugacy classes of the gis, describe the connected components of the space.

This talk will explain the following case/result: Spaces of r-branch point 3-cycle covers, of degree n, or their Galois closures
of degree n!/2, have one (resp. two) component(s) if r=n-1 (resp. rn).

Each space is determined by the type of natural θ functions they support. This improves a Fried-Serre formula on when sphere covers with odd-order branching lift to unramified Spin covers of the sphere. We will use the case n=4, to see these Θs and differentiate between their even and odd versions. Riemann used both for different purposes.

This is a special case of a general result about components of spaces of sphere covers. Hyperelliptic jacobians then appear as one case of a general problem entwining The Torsion Conjecture and the Regular Inverse Galois problem. A recent series of Ellenberg-Venkatesh-Westerland used these results, but only got to the hyperelliptic jacobian case.

Date:December 4, 2019
Time:1:45pm
Location:BLOC 220
Speaker:Guchao Zeng, Texas A&M University at Qatar
Title:Modular Equations and Traces of Singular Moduli over Function Fields
Abstract:In this talk, I will introduce the modular polynomials as well as the relation between j-invariants and class polynomials in classical number fields. And then I will give the corresponding theorem in function fields and derive the equation giving value to the trace of the class polynomial, which is a summation of a few j-invariants. This work is joint with A. El-Guindy, R. Masri and M. Papanikolas.