University of Chicago Number Theory Seminar

Winter 2014: Tuesday 1:30-2:50pm, E308


This is the homepage of the Number Theory Seminar at the University of Chicago. To get on or off the mailing list, you can either go to lists.uchicago.edu or contact Davide Reduzzi.

NOTE: the room for this quarter is E308.

Click here to see the location of Eckhart Hall, and here for directions to the University of Chicago.

Click here to see the schedule of previous quarters: Winter 2010 / Spring 2010 / Fall 2010 / Winter 2011 / Spring 2011 / Fall 2011 / Winter 2012 / Spring 2012 / Fall 2012 / Winter 2013 / Spring 2013 / Fall 2013 / Spring 2014

Winter 2015 Schedule

Date

Speaker

Title

January 7

Andrew Sutherland
(MIT)

The Sato-Tate conjecture for abelian varieties
The original Sato-Tate conjecture addresses the statistical distribution of the number of points on the reductions modulo primes of a fixed elliptic curve defined over the rational numbers. It predicts that this distribution can be explained in terms of a random matrix model, using the Haar measure on the special unitary group SU(2).... (Show Abstract)

January 14

Ronen Mukamel
(UChicago)

Billiards, Hilbert modular forms and explicit algebraic models for Teichmuller curves
For each real quadratic ring O, the Hilbert modular surface parametrizing principally polarized abelian varieties with real multiplication by O contains a Weierstrass curve W(O). The curve W(O) emerges from the study of billiards in polygons and is important in Teichmuller theory because the natural immersion into the moduli space of genus two curves is isometric.... (Show Abstract)

January 21

Preston Wake
(UChicago)

The p-adic Eichler-Shimura isomorphism
A theorem of Eichler and Shimura says that the space of cusp forms with complex coefficients appears as a direct summand of the cohomology of the compactified modular curve. Ohta has proven an analog of this theorem for the space of ordinary p-adic cusp forms with integral coefficients. Ohta's result has important applications in the Iwasawa theory.... (Show Abstract)

January 28

Keerthi Madapusi Pera
(Harvard)

The irreducibility of the moduli of polarized K3 surfaces
We show that the moduli of polarized K3 surfaces of fixed degree is irreducible in characteristic p>2. The key idea is to exhibit p-Hecke correspondences between the ordinary loci of moduli spaces of different degrees and so reduce to the case where the degree is not too divisible by p. For the construction of these correspondences, we make crucial use of.... (Show Abstract)

February 4

Robert Pollack
(Boston University)

On μ-invariants and congruences with Eisenstein series
For any irregular prime p, one has a Hida family of cuspidal eigenforms of level 1 whose residual Galois representations are all reducible. This family has already played a starring role in Wiles’ proof of Iwasawa’s main conjecture for totally real fields. In this talk, we instead focus on the Iwasawa theory of these modular forms in their own right. We will discuss new phenomena..... (Show Abstract)

February 11

Liang Xiao
(UC Irvine)

Slopes of the eigencurve over boundary disks
Despite the importance of eigencurve in the p-adic number theory, the geometry of the eigencurve is still poorly understood. The amazing calculation of Buzzard-Kilford in the case of p=2 suggests that the slopes of the eigencurve should behave reasonably well near the boundary of the weight space. In this talk, I will report on some evidence regarding this expectation..... (Show Abstract)

February 26 (Wed)
Note special day!
(2:30-4PM in E206)

Frank Calegari
(Northwestern Univ.)

The stable homology of congruence subgroups
(Joint seminar with Alg.Top. and Geom./Top.).
Let F be a number field. A stability result due to Charney and Maazen says that the homology groups Hd(SLN(OF),Z) (for d fixed) are independent of N for N sufficiently large. The resulting stable cohomology groups are intimately related to the algebraic K-theory of OF. In these talks, we shall explore the homology of the p-power congruence subgroups of SLN(OF) in fixed degree d as N becomes large. We show that the resulting homology groups consist of two parts: an “unstable” part which depends only on local behavior concerning how the prime p splits in F, and a “stable” part which contains global information concerning p-adic regulator maps. Our argument consists of two parts. The first part (which is joint work with Matthew Emerton) explains how to modify the homology of congruence subgroups in a suitable way (using completed homology) to obtain groups which are literally stable for large N..... (Show Abstract)

February 28 (Fri)
Note special day!
(2:30-4PM in E206)

March 4

Anders Södergren
(Univ. of Copenhagen)

Poisson statistics and the value distribution of the Epstein zeta function
In this talk I will discuss certain questions concerning the asymptotic behavior of the Epstein zeta function En(L,s) in the limit of large dimension n. In particular, I will describe the value distribution of En(L,s) for a random lattice L of large dimension n, giving partial answers to questions raised by Sarnak and Strömbergsson in their study of minima of En(L,s)..... (Show Abstract)

March 11

Yongqiang Zhao
(Univ. of Waterloo)

On sieve methods for varieties over finite fields
Although sieve methods in classical analytic number theory have a long and very fruitful history, its appearance in algebraic geometry is relatively new, and was introduced by Bjorn Poonen about ten years ago. In this talk, we will first discuss Poonen's sieve through a concrete example, then we will introduce a new interpolation technique to sieve methods..... (Show Abstract)

One may also want to check out:

  • Geometric Langlands Seminar Monday and Thursday 4:30pm;
  • Algebraic Geometry Seminar biweekly on Wednesday 4:30pm-6pm;
  • Northwestern University Number Theory Seminar Monday 4pm;
  • UIC Number Theory Seminar Tuesday 1pm.

    This page is maintained by Davide Reduzzi; it was shamelessly copied from Liang Xiao's page, which was shamelessly copied from Kiran Kedlaya's page, which in turn was shamelessly copied from Jason Starr's page, which in turn was shamelessly copied from Ravi Vakil's page, which in turn was shamelessly copied from Pasha Belorousski's page at the University of Michigan. For more sites with a similar pedigree, see Michael Thaddeus's list or Jim Bryan's list.