University of Chicago Number Theory Seminar

Fall 2013: Tuesday 1:30-2:50pm, room E 202

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 or contact Davide Reduzzi.

NOTE: the room for this quarter is Eckhart 202.

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

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.

    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 / Winter 2014

    When an abstract is available, click on "Show Abstract" to expand the abstract, or click on "Hide Abstract" to hide it.





    October 1

    Matthew Emerton

    Introduction to p-adic Hodge theory
    The talk is an introduction to p-adic Hodge theory aimed to graduate students.

    October 8

    Simon Marshall
    (Northwestern University)

    Endoscopy and cohomology growth on U(3)
    I will use the endoscopic classification of automorphic forms on U(3) to determine the asymptotic cohomology growth of families of complex-hyperbolic 2-manifolds.

    October 15

    Stefan Patrikis
    (Harvard Univ./MIT)

    Potential automorphy of regular self-dual motives
    I will describe joint work with Richard Taylor showing that the potential automorphy theorems of Barnet-Lamb, Gee, Geraghty, and Taylor continue to hold with purity hypotheses in place of the usual irreducibility hypotheses...(Show Abstract)

    October 22

    David P. Roberts
    (Univ. of Minnesota - Morris)

    Hypergeometric motives and their wild ramification
    Let α = (α1,..., αd) and β = (β1,..., βd) be tuples in (Q/Z)d with always αj ≠ βk. The datum (α,β) determines a classical hypergeometric function F(α,β;t), which is a multivalued function of tC - {0,1}. Underlying F(α,β;t) is a family H(α,β;t) of rank d motives. Monodromy about 0 and ∞ is regular with eigenvalues being exp(2πiβj) and exp(2πiαk) respectively....(Show Abstract)

    October 29

    Jerry Wang
    (Princeton University)

    Pencils of quadrics and the arithmetic of hyperelliptic curves
    In recent joint works with Manjul Bhargava and Benedict Gross, we showed that a positive proportion of hyperelliptic curves over Q of genus g have no points over any odd degree extension of Q. This is done by computing certain 2-Selmer averages and applying a result of Dokchitser-Dokchitser on the parity of the rank of the 2-Selmer groups in biquadratic twists. In this talk....(Show Abstract)

    November 5

    Wei Ho
    (Columbia University)

    Families of lattice-polarized K3 surfaces
    There are well-known explicit families of K3 surfaces equipped with a low degree polarization, e.g., quartic surfaces in P^3. What if one specifies multiple line bundles instead of a single one? We will discuss representation-theoretic constructions of such families, i.e., moduli spaces for K3 surfaces whose Neron-Severi groups contain specified lattices.....(Show Abstract)

    November 12

    Haruzo Hida

    Big image of automorphic Galois representations and congruence ideals
    In a work in progress with J. Tilouine, we show the existence of a principal congruence subgroup contained in the image of the Galois representation associated to a p-adic family of modular forms for GL(2) and GSp(4). This defines an ideal, called Galois level; we relate this ideal with congruence ideals and p-adic L-functions.

    November 19

    Eyal Goren
    (McGill University)

    Intersection theory on GSpin Shimura varieties and a conjecture of Bruinier and Yang
    This is joint work with F. Andreatta (Milano), B. Howard (Boston College) and K. Madapusi-Pera (Harvard). GSpin Shimura varieties are associated to quadratic forms over the rationals. They are Shimura varieties of Hodge type but not PEL type, except in rare circumstances, a fact that is a significant obstacle for understanding and utilizing their arithmetic.....(Show Abstract)

    November 26

    Zhiwei Yun
    (Stanford University)

    Moments of Kloosterman sums and modular forms
    Kloosterman sum is one of the most famous exponential sums in number theory. It is defined using a prime p (and another number). How do these sums vary with p? Ron Evans has made several conjectures relating the moments of Kloosterman sums for p to the p-th Fourier coefficient of certain modular forms. We sketch a proof of his conjectures.

    December 3

    Benjamin Howard
    (Boston College)

    Supersingular points on some orthogonal and unitary Shimura varieties
    To an orthogonal group of signature (n,2), or to a unitary group of any signature, one can attach a Shimura variety. The general problem is to describe the integral models of these Shimura varieties, and their reductions modulo various primes. I will give a conjectural description of supersingular points of the reduction in the orthogonal case, and a complete description of the supersingular points in the case of a unitary group of signature (2,2). This is joint work with G. Pappas.

    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.