University of Georgia
Department of Mathematics
Seminar Schedule
October 17– October 21, 2005
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.

MONDAY, October 17, 2005

Topology/Geometry
2:30-4:30pm, Room 303
No Meeting this week

Algebra
2:30-3:30pm., Room 410
Speaker: Daniel Nakano, University of Georgia
Title of talk: Cohomology of quantum groups I
Abstract: The main purpose of the two lectures is to demonstrate how to compute cohomology for quantum groups when l<h. This computation entails many beautiful results:

1) Realization of the ``restricted nullcone'' due to Carlson, Lin, Nakano and Parshall

2) Combinatorics involving the decomposition of the exterior algebra via the Steinberg representation. Our decomposition results makes use of MAGMA computations on root systems for exceptional Lie algebras.

3) Powerful vanishing results on line bundle cohomology proved via complex algebraic geometry (i.e. Grauert-Riemenschnieder theorem).

4) Normality results on the closures of nilpotent orbits due to Kraft-Procesi, Sommers, Broer, Kumar-Lauritzen-Thomsen.

Our results show that the cohomology ring is finitely generated. This allows us to define support varieties and compute the support varieties for quantum Weyl modules in the case when (l,p)=1 where p is any bad prime for the underlying root system.

This talk represents joint work with Christopher Bendel, Brian Parshall, and Cornelius Pillen.

Faculty and Graduate Social
3:00pm, Room 409
Coffee, Cookies, Tea

TUESDAY, October 18, 2005

VIGRE-Graduate Student Seminar
2:00p.m., Room 303
Speaker: Matt Boylan, University of South Carolina
Title of talk: Modular forms and partitions
Abstract: Modular forms naturally occur as generating functions for many objects of arithmetic interest such as central critical values of L-functions associated to elliptic curves over the rationals, representation numbers of positive definite quadratic forms, and partitions. The partition function, p(n), counts the number of non-increasing sequences of positive integers whose sum is n. In this talk, we discuss recent results on the distribution and arithmetic of p(n) modulo a positive integer M and some of the ideas from the theory of modular forms used to prove these results.

Number Theory
3:30-5:00pm., Room 304
Speaker: Matt Boylan, University of South Carolina
Title of talk: Non-vanishing of central critical values of modular L-functions modulo l.
Abstract: Let l be prime, let F(z) be a newform of weight 2k, let D be a fundamental discriminant, and L(F,D,s) be the L-series of F twisted by the Kronecker character of discriminant D. In this talk, I will show that if there are two D (subject to some local constraints) for which the algebraic part of the central critical value L(F,D,k) is not 0 mod l, then there are infinitely many such D. This result depends on non-vanishing results for the Fourier coefficients of half-integral weight modular forms modulo l which are of independent interest. I will discuss applications to elliptic curves and orders of Shafarevich-Tate groups. This is joint work with Scott Ahlgren (Univ. of Illinois).

WEDNESDAY, October 19, 2005

Algebraic Geometry
2:30-3:45pm, Room 410
Speaker: Valery Alexeev, University of Georgia
Title of talk: Torelli map and infinite grassmannians.
Abstract: I will begin with an observation that combinatorially the Torelli map M_g -> A_g near the boundary behaves like the "Chow quotient" of the Plucker embedding of an infinite grassmannian Gr(2,infty). Of course, this immediately reminds one of the even "more infinite" Sato-Segal grassmannian Gr(infty, infty/2) and the Krichever's construction. I will try to explain how the two stories are related.

Faculty and Graduate Social
3:00pm, Room 409
Coffee, Cookies, Tea

VIGRE-Algebra Group
3:45p.m., Room 302

THURSDAY, October 20, 2005

VIGRE-Feynman Diagrams
2:00pm, Room 326

VIGRE – Cardiac Physiology
2:00p.m., Room 640

VIGRE Algebraic Geometry Group
3:30 pm in Room 323

Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea, Cookies

Colloquium
3:30pm, Room 304
Speaker: Alexander Kleshchev, University of Oregon
Title of talk: Polynomial representations of GL(n)
Abstract: We trace the 120 year old history of polynomial representations of GL(n), which has its roots in classical invariant theory, through the work of Deruyts, Schur, Weyl, Gelfand-Tsetlin, Lusztig and others. In the end we will sketch a categorification of polynomial GL(n)-modules obtained recently by Brundan and the speaker.

FRIDAY, October 21, 2005

Probability Theory
2:30pm, Room 303
Speaker: Jie Yu, University of Georgia
Title of talk: Optimal hedging with basis risk