## 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**

**2010**

** ****Fall 2009**

** ****Spring 2009**

** ****Spring 2007**

** ****Fall 2006**

Spring 2006

**
**