Collaborative Number Theory Seminar at the CUNY Graduate Center

Co-organizers: Gautam Chinta, Brooke Feigon, Krzysztof Klosin, Maria Sabitova, Lucien Szpiro.

The seminar currently meets Fridays from 2:00 to 3:30 PM in Room 6421. The CUNY Graduate Center is located on Fifth Avenue, on the east side of the street, between 34th and 35th Streets in midtown Manhattan. For further information, please contact Maria Sabitova.

Fall 2019 Schedule:

September 6: Catherine Hsu (Bristol University)

Title: Eisenstein congruences and an explicit non-Gorenstein R=T

Abstract: In his seminal work on modular curves and the Eisenstein ideal, Mazur studied the existence of congruences between certain Eisenstein series and newforms, proving that Eisenstein ideals associated to weight 2 cusp forms of prime level are locally principal. In this talk, we begin by discussing several generalizations of Mazur's results to squarefree levels, focusing primarily on the non-principality of the Eisenstein ideal in the anemic Hecke algebra associated to elliptic modular forms of weight 2 and trivial Nebentypus. We then discuss some work in progress, joint with Preston Wake and Carl Wang-Erickson, that establishes an algebraic criterion for having R=T in a certain non-Gorenstein setting.

November 8: Gunther Cornelissen (Utrecht)

Title: Is there a prime number theorem in algebraic groups?

Abstract: The prime number theorem reveals something simple about the otherwise difficult world of prime numbers: the probability of finding a prime number amongst the first N integers is approximately log(N) (and the error relates to the Riemann hypothesis). In the talk, we will first explain a similar statement about counting irreducible polynomials modulo a prime number p, amongst all polynomials of a given degree modulo p. Then we will interpret this result as a statement about a dynamical system: it says something about the orbit distribution under iteration of a specific map (“Frobenius”) on a specific algebraic group (“the additive group”). We then study the generalisation to arbitrary endomorphisms of arbitrary algebraic groups. The pictures of orbit size distribution sometimes look like those of a non-ergodic system. If the prime number theorem fails, can we rescue the Riemann hypothesis? (Joint work with Jakub Byszewski and Marc Houben)

Seminar schedule in past semesters:

Spring 2019
Fall 2018

Fall 2017
Spring 2017

Fall 2016

Spring 2016
Fall 2015
Spring 2015

Fall 2014

Spring 2014
Fall 2013

Spring 2013

Fall 2012
Spring 2012

Fall 2011

Spring 2011
Fall 2009
Spring 2009
Spring 2007
Fall 2006
Spring 2006