Seminar Schedule
October 2 - 6, 2006
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.
MONDAY, October 2, 2006
Topology
2:30pm, Room 304
Speaker: TBA
Title of talk: TBA
Algebra
2:30pm, Room 410
Speaker: Emilie Weisner, UGA
Title of talk: Cohomology of Category $\mathcal O$ for
the Virasoro algebra
Abstract: I will talk about some results on the blocks of the
category $\mathcal O$ for the Virasoro algebra. BGG resolutions exist for the
simple modules in $\mathcal O$, which allow us to compute $Ext^n_ {\mathcal
O} (M(\mu), L(\lambda))$, for a Verma module $M(\mu)$ and a simple module $L(\lambda)$.
Using the theory of highest weight categories developed by Cline, Parshall,
and Scott, we can also compute $Ext^n_{\mathcal O} (L(\lambda), L(\mu))$ and
show certain algebras are Koszul.
Faculty and Graduate Student Social
3:00pm, Room 409
Coffee, Cookies, Tea
TUESDAY, October 3, 2006
VIGRE
Graduate Student Seminar
2:00pm, Room 302
Speaker: Bobbe Cooper, University of Georgia
Title of talk: Tips for Surviving Graduate School
Abstract: In this talk I will discuss strategies for managing
your time and being productive in graduate school -- while keeping your sanity.
We'll talk about balancing school and personal life, organizing office space,
dealing with the multiple strains on your time, and getting motivation for long-term
projects and day-to-day tasks. I'll also describe some nitty-gritty practical
ways to start and continue mathematical research. This talk should be accessible
to first-year graduate students.
Special Number Theory Talk
3:30pm, Room 304
Speaker: R. Parimala, Emory
Title of talk: Rational points on homogeneous spaces.
Abstract: Let G be a connected linear algebraic group defined
over a field and X a principal homogeneous space under G. There are open questions
concerning whether the existence of a zero cycle of degree one implies the existence
of a rational point on X. We discuss the case of number fields where these questions
admit a positive response and explain known results in a general context.
Analysis
3:30pm, Room 222
Speaker: Neil Lyall, University of Georgia
Title of talk: On a Theorem of Sarkozy I: Introduction
(continued)
Abstract: A theorem of Sarkozy and Furstenberg states that
the difference set A-A of any given subset A of positive (upper) density in
the integers necessarily contains a square.
In last week's seminar we discussed this theorem, indicated how it relates to Szemeredi's Theorem, and announced our strengthening of Sarkozy's theorem:
There exists an integer M=M(A) such that any collection of M consecutive integers necessarily contains an integer whose square is an element of A-A.
We hope to do the following:
1. Conclude arguments that establish the analogous result without the "square" requirement; namely the existence of an integer M=M(A) such that A-A intersects every interval of integers of length M.
2. Prove Roth's theorem (Szemeredi's theorem for arithmetic progressions of
length three).
WEDNESDAY, October 4, 2006
Algebraic Geometry
2:30pm, Room 410
Speaker: Elham Izadi, University of Georgia
Title of talk: New correspondences on curves and Prym-Torelli,
I
Abstract: A correspondence on a curve C is another curve embedded
in the cartesian product of C with itself. In this first talk I will explain
a geometric way of constructing new correspondences on some special curves.
In a second talk I will show how these correspondences satisfy polynomial equations
with integer coefficients and give rise to new conterexamples to the Prym-Torelli
problem.
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea, Cookies
Arithmetic
Geometry/Number Theory
3:30pm, Room 304
Speaker: Andrew Granville, Montreal
Title of talk: Rational and integral points on quadratic
twists of hyperelliptic curves.
Abstract: Elkies' proof that abc implies Faltings theorem (that
there are finitely many rational points on an algebraic curve X of genus >1)
does effectively bound the height of rational points though in terms of the
height of the Belyi map (from X to P^1) which tends to be very large. However
by running through certain (carefully selected) families of curves we can have
more control over the Belyi maps, and thus obtain more useful height bounds.
THURSDAY, October 5, 2006
VIGRE-Algebraic Geometry
2:00pm, Room 410
Wavelets and Splines
2:30pm, Room 524
Speaker: Dr. Jie Zhou, University of Georgia
Title of talk: Image Compression by Wavelets with dilation=3
Abstract: We present a new method to construct orthonormal
wavelets with dilation=3
and apply our wavelets for image compression. We show that we can compress
images at compression ratio 128:1 with excellent reconstruction.
Faculty and Graduate Social
3:00pm., Room 409
Coffee, Tea, Cookies
Colloquium
3:30pm, Room 304
Speaker: Andrew Granville, Montreal
Title of talk: Various pretentious characters
Abstract: We explain how certain key results in analytic number
theory can be rephrased in terms of pretentiousness, and discuss some joint
results with K. Soundararajan motivated by this new concept.
VIGRE - Quantum Mechanics
4:45, Room 410
David Finkelstein will speak on Homotopies to algebraic quantum gravity.
FRIDAY, October 6, 2006
Probability Theory
2:30pm, Room 323
Speaker: Lirong Yu, University of Georgia
Title of talk: Optimal control of switching diffusions
(cont.)
Geometry
2:30pm, Room 410
Speaker: TBA
Title of talk: TBA
VIGRE-Algebra
2:30pm, Room 304