Collaborative Number Theory Seminar at the CUNY Graduate CenterCoorganizers: Gautam Chinta, Brooke Feigon, Krzysztof Klosin,
Maria Sabitova,
Lucien Szpiro. Fall 2015 Schedule:October 23: Tom Tucker (University of Rochester) Title: The dynamical gcd problem over function fields Abstract:
A classic result of Bugeaud, Corvaja, and
Zannier shows that if a and b are
multiplicatively independent integers and e >
0, then October 30: Rachel Ollivier (University of British Columbia) Title:
Torsion pairs in the representation theory of
IwahoriHecke algebras Abstract: Given a padic reductive group G and its
(prop) IwahoriHecke algebra H, we are interested
in the link between the category of representations
of G and the category of Hmodules. When the field
of coefficients has characteristic zero, this link
is well understood by work of Bernstein and Borel.
When the field has characteristic p, this link is
much more involved and is still quite mysterious. We
develop an approach to this question by defining a
canonical torsion pair in the category of Hmodules.
This is joint work with Peter Schneider. November 6: Joe KramerMiller (CUNY)
November 13: Wade Hindes (CUNY)
November 20: Moshe
Adrian (CUNY Queens college)
December 18: Manish Patnaik (University of Alberta) Title: Cuspidal Eisenstein Series on Loop Groups over Function Fields
Abstract:
I will explain the construction of cuspidal
Eisenstein series on loop groups over function
fields starting from both ‘positive’ and ‘negative’
maximal parabolics. The positive variant results in
an entire function, whereas the negative one— which
was first introduced by A. Braverman and D. Kazhdan—
produces a (conjecturally) meromorphic object.
A functional equation can also be proven that
relates the positive and negative series and in
which Lfunctions of cusp forms (on finite
dimensional groups) appear.
