NTS Spring 2015 Abstract

Jan 29

Lillian Pierce

Averages and moments associated to class numbers of imaginary quadratic fields

Given an imaginary quadratic field of discriminant d, consider the p-part of the associated class number for a prime p. This quantity is well understood for p=2, and significant results are known for p=3, but much less is known for larger primes. One important type of question is to prove upper bounds for the p-part. Desirable upper bounds could take several forms: either “pointwise” upper bounds that hold for the p-part uniformly over all discriminants, or upper bounds for the p-part when averaged over all discriminants, or upper bounds for higher moments of the p-part. This talk will discuss recent results (joint work with Roger Heath-Brown) that provide new upper bounds for averages and moments of p-parts for odd primes.

Feb 05

Keerthi Madapusi

Heights of special divisors on orthogonal Shimura varieties

The Gross-Zagier formula relates two complex numbers obtained in seemingly very disparate ways: The Neron-Tate height pairing between Heegner points on elliptic curves, and the central derivative of a certain automorphic L-function of Rankin type. I will explain a variant of this in higher dimensions. On the geometric side, the intersection theory will now take place on Shimura varieties associated with orthogonal groups. On the analytic side, we will find Rankin-Selberg L-functions involving modular forms of half-integral weight. This is joint work with Fabrizio Andreatta, Eyal Goren and Ben Howard.

Feb 12

SPEAKER

TITLE

ABSTRACT

Feb 19

David Zureick-Brown

The canonical ring of a stacky curve

Coming soon...

Feb 26

Rachel Davis

Coming soon...

Coming soon...

Mar 05

Hongbo Yin

Some non-congruence subgroups and the associated modular curves

We give some new non-congruence subgroups which is close to the Fermat groups but with very different properties.