Number Theory Seminar

Date Time 
Location  Speaker 
Title – click for abstract 

01/24 1:15pm 
BLOC 220 
Matt Young Texas A&M University 
Equidistribution of Eisenstein series
I will discuss recent work on the behavior of Eisenstein series on the modular surface, restricted to geodesic segments. Abstract 

01/31 1:15pm 
BLOC 220 
Andrew Bridy Texas A&M University 
The cycle structure of unicritical polynomials in finite fields
Let f(x) = x^k+a in Z[x] for k \geq 2. Consider the family of dynamical systems given by the action of f on F_p as p varies among primes. The question of how and in what sense this family approximates a random family of dynamical systems has been studied extensively, motivated in part by Pollard's "rho" algorithm for integer factorization. We show that for most choices of a, the cycle structure in this family is "as random as possible" in an appropriate sense. As a corollary, we show that most members of these families have many cycles. This is joint work with Derek Garton. Abstract 

02/28 1:15pm 
BLOC 220 
WeiLun Tsai Texas A&M University 
Analytic formulas for Stark units in quadratic extensions of totally real cubic fields
In this talk, we will explain how Stark units in certain quadratic extensions of totally real cubic fields can be evaluated explicitly in terms of values of the Barnes triple Gamma function at algebraic arguments. This is joint work with Adrian BarqueroSanchez and Riad Masri.
Abstract 

03/07 1:15pm 
BLOC 220 
Souvik Goswami Texas A&M University 
Higher arithmetic Chow groups
We give a new definition of higher arithmetic Chow groups for smooth projective varieties defined over a number field, which is similar to Gillet and Soulé's definition of arithmetic Chow groups. We also give a compact description of the intersection theory of such groups. A consequence of this theory is the definition of a height pairing between two higher algebraic cycles, of complementary dimensions, whose real regulator class is zero. This description agrees with Beilinson's height pairing for the classical arithmetic Chow groups. We also give examples of the higher arithmetic intersection pairing in dimension zero that, assuming a conjecture by Milnor on the independence of the values of the dilogarithm, are non zero. This is a joint work with José Ignacio BurgosGil from ICMAT, Spain. Abstract 

03/28 1:15pm 
BLOC 220 
Solly Parenti University of Wisconsin 
Unitary CM fields and the Colmez conjecture
In 1993, Pierre Colmez conjectured a relation between the Faltings height of a CM abelian variety and certain log derivatives of Lfunctions associated to the CM type, generalizing the classical ChowlaSelberg formula. I will discuss how we can extend the known cases of the conjecture to a certain class of unitary CM fields using the recently proven average version of the conjecture. Abstract 

04/11 1:15pm 
BLOC 220 
Alan Haynes University of Houston 
TBA 

04/18 1:15pm 
BLOC 220 
Shuhui Shi University of Rochester 
TBA 
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The calendar for this seminar is maintained by
Matt Papanikolas.