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