Seminar Schedule
January 15 - 19, 2007
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.
MONDAY, January 15, 2007
University Holiday
TUESDAY, January 16, 2007
VIGRE-Graduate
Student Seminar
2:00pm, Room 304
Speaker: Michael Guy, University of Georgia
Title of talk: A First Look at Moduli Spaces in Algebraic
Geometry
Abstract: Like other subjects, algebraic geometry has many
"classification problems." I will give a beginner's first look at
moduli spaces and their role in the classification and understanding of curves.
This will be a completely elementary talk.
Faculty and Graduate Student Social
3:00pm, Room 409
Coffee, Cookies, Tea
Job Candidate Talk
3:30pm, Room 304
Speaker: Kevin Purbhoo, University of British Columbia
Title of talk: Horn's conjecture
Abstract: I will talk about two problems, which at first glance
appear to be unrelated.
The first is a linear algebra problem that dates back to the 19th century, known
as the Hermitian sum problem. It asks: If the eigenvalues of two Hermitian matrices
are known, what are the possible eigenvalues of their sum? The second is a fundamenatal
question concerning the geometry and combinatorics of Grassmannians and related
spaces: When does a collection of Schubert varieties (in general position) have
a non-empty intersection?
Both these questions are interesting in their own right, and have a long and rich history. However, in the 1990s it was shown that these two problems are connected in deep and remarkable ways. This revelation gave rise the first complete solution to the Hermitian sum problem [Klyachko 1994], and proved that this solution satisfied a mysterious recursion which had been conjectured by Horn in the 1960s [Knutson-Tao 1999]. To the uninitiated, Horn's conjecture may seem a little strange. However, I will explain why it is at the heart of this story, and how our understanding of it sheds light on the whole picture. Finally I will discuss a few of the directions in which these results have been refined and generalized.
WEDNESDAY, January 17, 2007
Algebraic Geometry
2:30pm, Room 410
No Meeting this week
Faculty and Graduate Student Social
3:00pm, Room 409
Coffee, Cookies, Tea
Number
Theory/Arithmetic Geometry
3:30pm, Room 304
No Meeting this week
Job Candidate Talk
3:30pm, Room 304
Speaker: Neil Lyall, University of Georgia
Title of talk: Some additive properties of dense subsets
of the integers
Abstract: A theorem of Sarkozy and Furstenberg states that
if $A$ is a subset of $Z$ with positive upper Banach density, then the set of
quadratic return times (naturals numbers whose square intersect the difference
set of $A$) is non-empty.
Using Fourier analysis we prove that the set of all $\epsilon$-optimal quadratic return times is syndetic for all $\epsilon$ and obtain uniform lower bounds for the density of these return times.
We hope to also discuss some extensions of this result as well as give some
background and motivation for these results (and the use of Fourier analysis
in additive combinatorics in general).
VIGRE – Quantum Mechanics
4:45pm, Room 302
THURSDAY, January 18, 2007
VIGRE – ODE
2:00pm, Room 326
VIGRE – Branchvarieties
2:00pm, Room 304
Faculty and Graduate Student Social
3:00pm, Room 409
Coffee, Cookies, Tea
Job Candidate Talk
3:30pm, Room 304
Speaker: Lee Deville, Courant Institute of Mathematical Sciences
Title of talk: Regularity and synchrony in stochastic systems
Abstract: It has been observed in many contexts that coupling
stochastic systems can make their dynamics more reliable, and that networks
of stochastic elements can become synchronous. We will analyze a few model problems
and characterize mechanisms which produce reliable and synchronous behavior.
We will describe applications of these mechanisms to neuron firing, excitable
reaction-diffusion equations, and motor protein dynamics.
FRIDAY, January 19, 2007
VIGRE – Algebra
2:30pm, Room 304
Geometry
2:30pm, Room 410
No meeting this week
Faculty and Graduate Student Social
3:00pm, Room 409
Coffee, Cookies, Tea
VIGRE - Hodge Theoretic questions in Algebraic Geometry
3:30pm, Room 410
No Meeting this week
Job Candidate Talk
3:30pm, Room 304
Speaker: Alina Marian, Yale
Title of talk: Verlinde formulas on moduli spaces of vector
bundles via Quot schemes.
Abstract: I will describe the relation between intersection
products on the moduli space of coprime rank and degree stable vector bundles
on a smooth curve, and a class of enumerative intersections on the space of
maps from the curve to a suitable Grassmannian. This relationship yields painlessly
the Verlinde formulas on the moduli space of bundles, computing the dimensions
of spaces of sections of tensor powers of the determinant bundle. This work
is joint with Dragos Oprea.