University of Georgia
Department of Mathematics

Seminar Schedule
November 13- November 17, 2006

All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.

 

MONDAY, November 13, 2006

Topology
2:30pm, Room 304
Speaker: Gordana Matic, University of Georgia
Title of talk: Contact topology and the invariant of Ozsvath and Szabo, continued

Algebra
2:30pm, Room 410
Speaker: Daniel K. Nakano, University of Georgia
Title of talk: Projective Modules over Frobenius Kernels and Finite Chevalley Groups
Abstract: Let $G$ be a reductive algebraic group scheme over a field of characteristic $p0$ (e.g. $G=\text{GL}_{n}$), and $M$ is a finite-dimensional $G$-module. One can differentiate this action to consider $M$ as a module for ${\mathfrak g}$ the Lie algebra of $G$. On the other hand one can restrict the action to the finite subgroup $G({\mathbb F}_{p})$ (e.g. $\text{GL}_{n}({\mathbb F}_{p})$ where ${\mathbb F}_{p}$ is the finite field of $p$ elements). In 1987, Parshall conjectured that under these assumptions, if $M$ a projective ${\mathfrak g}$-module then $M$ is a projective $G({\mathbb F}_{p})$-module. This conjecture has a natural generalization for higher Frobenius kernels $G_r$ and finite Chevalley groups $G({\mathbb F}_{q})$ where $q=p^{r}$. In this talk, I will present recent results with Zongzhu Lin on a solution to this general conjecture and its applications towards relating the representation/cohomology theory of Frobenius kernels and finite Chevalley groups.


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


TUESDAY, November 14, 2006

VIGRE Graduate Student Seminar
2:00pm, Room 302
Speaker: Andrew Sornborger, University of Georgia
Title of talk: TBA

Arithmetic Geometry/Number Theory Special Seminar
2:00pm., Room 410
Speaker: David Sinnou, Univeristy of Paris 6
Title of talk: Heights on elliptic curves.

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

Colloquium
3:30pm, Room 304
Speaker: David Sinnou, University of Paris 6
Title of talk: Transcendental numbers and diophantine geometry.
Abstract: Starting with a few historical problems on transcendal numbers, we shall explain how the tools developed for transcendental number theory can now be used to tackle modern problems of arithmetic geometry.

Analysis
3:30pm, Room 222
Speaker: Shuzhou Wang, University of Georgia
Title of talk: Introduction to quantum permutation group
Abstract: The quantum permutation group of the space of n point is the quantum automorphism group of the space. Unlike the classical situation of the permutation group, the algebra for the quantum permutation group of the n point space is infinite dimensional if n is at least 4, and the fusion/decomposition rules for its irreducible representations are the same as those for the Lie group SO(3) for different n, and it is simple as a quantum group. Study of quantum subgroups of the quantum permutation group such as the quantum automorphism groups of finite graphs and leads to new compact quantum groups.

Though there is a rather large literature on the quantum permutation group, there are still many fundamental questions. For instance, how to construct the models of its irreducible representations? How to classify its simple quantum subgroups? etc.

I will try to make this series of talks as self-contained as possible, starting from basic notions in the theory of compact quantum groups, and explain some of the main results and main problems on the quantum permutation group.

WEDNESDAY, November 15, 2006

Algebraic Geometry
2:30pm, Room 410
Speaker: William Graham (UGA)
Title: Algebraic cycles and completions of equivariant K-theory

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


THURSDAY, November 16, 2006

VIGRE-Algebraic Geometry
2:00pm, Room 410

Wavelets and Splines
2:30pm, Room 524
No Meeting this week

VIGRE - Quantum Mechanics
5:15pm, Room 410

 

FRIDAY, November 17, 2006

Probability Theory
2:30pm, Room 323
Speaker: David Prager, University of Georgia
Title of talk: Control of systems with jump Markov disturbances

Geometry
2:30pm, Room 410
Speaker: Sa'ar Hersonsky, University of Georgia
Title of talk: TBA

VIGRE-Algebra
2:30pm, Room 304