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 3209. 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 2017 Schedule:

Spetember 8: Peter Fiebig (FAU Erlangen-Nürnberg)

Title: Torsion primes in modular representation theory

Abstract: The recent quite unexpected appearance of torsion primes in the representation theory of modular algebraic groups by G. Williamson provides new challenges for representation theorists, some of them of number theoretic nature. I'd like to give an overview on the torsion prime problem and propose a new approach that translates the problem into a categorical framework in terms of (elementary) sheaf theory on partially ordered spaces.

November 17
: Claire Burrin (Rutgers University)

Title: Dedekind sums for cofinite Fuchsian groups

Abstract: Dedekind sums, studied since the late 19th century, are closely related to an amazing variety of objects ranging through combinatorics, geometry, number theory, and physics. Among those, we simply mention the discriminant form from the classical theory of modular forms, and winding and linking numbers for modular geodesics. For each cusp of a cofinite Fuchsian group, there is a natural construction from the theory of automorphic forms that can be used to define generalized Dedekind sums. We will show that these generalized Dedekind sums obey certain reciprocity laws, and discuss their relation to winding numbers for closed geodesics on hyperbolic surfaces.

December 1: Valentijn Karemaker (University of Pennsylvania)

Title: Dynamics of Belyi maps

Abstract: A (genus 0) /Belyi map/ is a finite map from the projective line to itself, branched exactly at 0, 1, and infinity. Such maps can be described combinatorially by their generating systems. Assuming further that 0, 1, and infinity are both fixed points and the unique ramification points above 0, 1, and infinity respectively yields /dynamical Belyi maps/, since the resulting maps can be iterated and will therefore exhibit dynamical behaviour. In this talk, we will discuss several results on the dynamics, reductions, and monodromy of dynamical Belyi maps, and the interplay between these. (This is joint work with J. Anderson, I. Bouw, O. Ejder, N. Girgin, and M. Manes.)