The University of Chicago - Number Theory Seminar

Fall 2014: Tuesday 1:30-2:50pm, Eckhart 312


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 E 312!

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 the previous quarter: Spring 2014

Fall 2014 Schedule

Date

Speaker

Title

September 30

Joël Bellaïche
(Brandeis)

Modular forms mod p
Starting as a conceptual tool to explain Ramanujan's congruences involving the tau function, the theory of modular forms modulo a prime p experienced a rapid development in the 70's and 80's with the works of Atkin, Swinnerton-Dyer, Serre, Tate and many others. Then this development almost stopped for two decades, leaving some of the most fundamental questions unanswered..... (Show Abstract)

October 7

Giovanni Rosso
(Columbia, KU Leuven)

Derivative of the symmetric square p-adic L-function via pull-back formula
Let f be a weight k modular form Steinberg at p. Under certain hypotheses on the conductor of f, we give a formula for the derivative at s = k - 1 of the symmetric square p-adic L-function of f, thus proving a conjecture of Benois on trivial zeros. Crucial is the construction of the p-adic L-function by Böcherer and Schmidt which we will recall.

October 10 (Fri)
Note special day!
2:30-4PM, in Ry-358

Yiwei She
(UChicago)

The Shafarevich conjecture for K3 surfaces
Let K be a number field, S a finite set of places of K, and g a positive integer. Shafarevich made the following conjecture for higher genus curves: the set of isomorphism classes of genus g curves defined over K and with good reduction outside of S is finite. In 1983, Faltings proved this conjecture for curves and the analogous conjecture for polarized abelian surfaces.... (Show Abstract)

October 14

Michael Lipnowski
(Duke)

Growth of torsion in the cohomology of arithmetic groups
We explain how to use spectral methods, specifically (twisted) analytic torsion, to study torsion in the cohomology of arithmetic groups. We describe a result, joint with Bergeron, proving growth of twisted analytic torsion. This allows one to show that torsion in the cohomology of certain "base-changed" arithmetic groups is abundant.

October 21

Carl Wang Erickson
(Brandeis)

Potentially semi-stable pseudodeformation rings
Let R be a deformation ring of representations of an absolute Galois group of a p-adic local field K, and let L be a finite extension of K. Kisin produced a quotient of R corresponding to representations which have bounded Hodge-Tate weights and are semi-stable after restriction to L. We will discuss an analogous result where R is replaced by a deformation ring of pseudorepresentations.... (Show Abstract)

October 23 (Thur)
Note special day!
3-4PM, in E-308

Joint Geom/Top Sem.

Darren Long
(UC Santa Barbara)

Geometric configurations of primes
A number field that contains a sufficiently large set of integers whose pairwise differences are all either units or generate prime ideals with a suitable property, has class number 1. Such sets of integers - which we call "Lenstra-Hurwitz cliques" - are surprisingly easy to find, and let us show that many number fields have class number 1.

October 28

George Boxer
(Harvard)

Torsion in the coherent cohomology of Shimura varieties and Galois representations
I will explain how to attach Galois representations to Hecke eigensystems in the coherent cohomology of the special fibers of certain good reduction Shimura varieties. As an application I will explain a new proof of cases of a recent theorem of Scholze on Galois representations associated to certain torsion classes in the Betti cohomology of arithmetic locally symmetric spaces.... (Show Abstract)

November 4

Chan-Ho Kim
(Univ. of California, Irvine)

November 11

Tonghai Yang
(Univ. of Wisconsin, Madison )

November 18

Bryden Cais
(Univ. of Arizona, Tucson)

November 25

Cheng-Chiang Tsai
(Harvard)

Related seminars:

  • Geometric Langlands Seminar Monday and Thursday 4:30pm;
  • Algebraic Geometry Seminar on hiatus during Fall 2014;
  • Northwestern University Number Theory Seminar Monday 4pm;
  • UIC Number Theory Seminar Tuesday 11am.

    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.