Seminar Schedule
September 25 - September 29, 2006
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.
MONDAY, September 25, 2006
Topology
2:30pm, Room 304
Speaker: Tara S. Holm, Cornell University
Title of talk: Topology of symplectic quotients
Abstract: I will talk about the topology of symplectic (and
other) quotients. I will review some background from symplectic geometry, the
construction of symplectic quotients, and the basic facts about their topology.
This theory can be used to compute a wide variety of invariants, and has applications
to representation theory, combinatorics and mathematical physics. As time permits,
I will discuss several of these applications.
Algebra
2:30pm, Room 410
No meeting this week
Faculty and Graduate Student Social
3:00pm, Room 409
Coffee, Cookies, Tea
TUESDAY, September 26, 2006
VIGRE
Graduate Student Seminar
2:00pm, Room 302
Speaker: Tara Holm, Cornell University
Title of talk: The combinatorics of moment polytopes
Abstract: I will discuss a problem that lies in the intersection
of symplectic geometry and combinatorics. The symmetries of a symplectic manifold
are reflected in its moment polytope. There is a dictionary translating the
geometry into combinatorics, and vice versa. I will start with the definition
of a polytope, describe enough symplectic geometry to motivate the moment polytope,
and then I will discuss several of the dictionary entries.
Analysis
3:30pm, Room 222
Speaker: Neil Lyall, University of Georgia
Title of talk: On a Theorem of Sarkozy I: Introduction
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.
We shall, in the second of these talks, present the following strengthening of this result:
There exists an integer K=K(A) such that any collection of K consecutive integers necessarily contains an integer whose square is an element of A-A.
The intent of the first talk is to be an introduction. We plan to discuss:
1. Different versions of Szemeredi's Theorem and how Sarkozy's
theorem relates to these
2. The (much simpler) continuous analogue of our result, showcasing
a beautiful argument of Bourgain
3. The proof of Roth's theorem (Szemeredi's theorem for arithmetic
progressions of length three), showcasing density increment
arguments
WEDNESDAY, September 27, 2006
Algebraic Geometry
2:30pm, Room 410
No meeting this week
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea, Cookies
Arithmetic
Geometry/Number Theory
3:30pm, Room 304
Speaker: Shahed Sharif, (Niagara University).
Title of talk: Period and index of genus one curves over
number fields.
Abstract: The period and index of a curve are two numbers which
measure the failure of a curve to have points. Lichtenbaum in the 60's proved
divisibility conditions that the genus, period, and index must satisfy. We will
show that for genus one curves over number fields containing certain roots of
unity, all possible periods and indices occur, and consequences for the size
of Tate-Shafarevich groups of elliptic curves. This is joint work with P. Clark.
THURSDAY, September 28, 2006
VIGRE-Algebraic Geometry
2:00pm, Room 410
Wavelets and Splines
2:30pm, Room 524
Speaker: Alexander Petukhov., University of Georgia
Title of talk: Method of Virtual Components for Wavelet
Frames
Abstract: This talk is based on a joint paper with M. J. Lai
which is recently accepted for publication. For a wavelet frame with a given
approximation order, we present a method for parametric description and construction
of all dual analysis operators(filter bank) with the maximum number of vanishing
moments.
Faculty and Graduate Social
3:00pm., Room 409
Coffee, Tea, Cookies
Colloquium
3:30pm, Room 304
Speaker: Adam Koranyi, Herbert H Lehman College (CUNY)
Title of talk: Homogeneous operators On Hilbert Spaces
With Reproducting Kernel
Abstract: This will be about joint work with Gadadhar Misra.
An operator T on a Hilbert space is called homogeneous (with respect to the
unit disc D) if its spectrum is contained in the closure of D and g(T) is unitarily
equivalent to T for every Mobius transformation g. These operators have interesting
properties, but not overly many examples of them have been known until now.
In the talk a family of such operators depending on countably many continuous
parameters will be constructed. The construction is explicit and elementary,
but in its background there are results about homogeneous holomorphic vector
bundles. It will be attempted to explain these connections.
VIGRE - Quantum Mechanics
4:45pm, Room 410
Retirement Dinner honoring Dr. Ken Johnson
Georgia Center
5:30pm, Cash Bar, 6:30pm, Dinner
For additional information, please contact Julie McEver, 706-542-2038.
FRIDAY, September 29, 2006
Probability Theory
2:30pm, Room 323
Speaker: Lirong Yu, University of Georgia
Title of talk: Optimal control of switching diffusions
Geometry
2:30pm, Room 410
Speaker: Mohammad Ghomi, Georgia Tech
Title of talk: Relative isoperimetric inequality
outside a convex body
Abstract: We prove that the area of a hypersurface which traps
a given volume outside of a convex body in Euclidean n-space must be greater
than or equal to the area of a hemisphere trapping the given volume on one side
of a hyperplane. This result generalizes the classical isoperimteric inequality.
The proof is based on a sharp estimate for total positive curvature of hyperurfaces
whose boundary lies on a convex body and meets that body orthogonally from the
outside. These results have been obtained in joint work with Jaigyoung Choe
and Manuel Ritore.
VIGRE-Algebra
2:30pm, Room 304