Collaborative Number Theory Seminar at the CUNY
Co-organizers: Gautam Chinta, Brooke Feigon, Krzysztof Klosin,
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:
8: Peter Fiebig (FAU
Torsion primes in modular representation theory
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
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.
Karemaker (University of Pennsylvania)
Dynamics of Belyi maps
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.)