Seminar Schedule
November 12 - November 16, 2007
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.
MONDAY, November 12, 2007
Algebra
2:30pm, Room 410
Speaker: Jon Carlson, University of Georgia
Title of talk: Jordan types for module over group algebras
Abstract: We discuss some constructions for stratifying modules over the modular group algebra of an elementary abelian group of order p2. This is joint work with Eric Friedlander and Andrei Suslin.
Topology
2:30pm, Room 303
Speaker: Justin Manning, University of Georgia
Title of talk: Myers's Theorem on Curvature and Compactness
Abstract: I'm going to describe sectional curvature and Ricci curvature on Riemannian manifolds, and state and prove Myers's Theorem, which allows us to determine that a manifold is compact if we have a positive lower bound on its Ricci curvature.
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea, Cookies
TUESDAY, November 13, 2007
VIGRE - Graduate Student Seminar
2:00pm, Room 304
Speaker: Benjamin Jones, University of Georgia
Title of talk: Schubert Calculus and Enumerative Geometry
Abstract: We introduce some ideas from classical enumerative geometry and discuss the connection to what is known as Schubert Calculus. A question we will discuss is ``How many lines in 3-dimensional space meet 4 generic lines?'' The 20th century answer to this question lies in understand the cohomology ring of an important class of algebraic varieties called Grassmannians.
FRG Analysis and Additive Combinatorics Working Group
3:30pm, Room 410
WEDNESDAY, November 14, 2007
Algebraic Geometry
2:30pm, Room 410
Speaker: Maxim Arap, University of Georgia
Title of talk: Singular Symplectic Moduli Spaces
Abstract: Irreducible symplectic manifolds appear as factors in the Bogomolov's decomposition of a compact Kahler manifold with the vanishing first Chern class. The decomposition theorem has been known since 1970's, but up to this date there are very few known examples of irreducible symplectic manifolds. Except for the Fano variety of lines in a cubic four-fold of Beauville and Donagi, all known examples arise as moduli spaces of sheaves on an abelian or a K3 surface. A new class of examples was discovered by O'Grady in 1999, when he showed how to desingularize a 10-dimensional moduli space of sheaves on a K3 surface. O'Grady asked whether symplectic desingularizations exist for other moduli spaces of sheaves on a K3 or abelian surface. Kaledin, Lehn, and Sorger answered this question completely in 2006 and their answer will be the topic of my presentation.
Faculty and Graduate Student Social
3:00pm, Room 409
Coffee, Cookies, Tea
Arithmetic Geometry/Number Theory
3:30pm, Room 304
Speaker: TBA
Title of talk: TBA
Abstract: TBA
Mathematical Physics
3:45pm, Room 302
Speakers: Brad Bassler and Robert Varley, University of Georgia
Title of talk: Caratheodory's formulation of thermodynamics, cont.
Math Club Talk
5:00-6:00, Boyd 304
Speaker: Janice Wethington, National Security Agency
Title of talk: Factoring Polynomials Over Finite Fields.
Abstract: The topic of polynomials over finite fields is basic to the study of cryptography. Certainly, we would want to know when one is irreducible or how it might factor into irreducibles over the field of interest. This talk starts with a short review of finite fields and a look at Stickelberger's Theorem. Then I will give recent results by NSA mathematicians on factoring polynomials over finite fields. This talk is designed to be accessible by undergraduate math majors.
THURSDAY, November 15, 2007
Applied Math
2:00pm, Room 302
Speaker: David Roach, Murray State University, Kentucky
Title of talk: Wavelet Parametrization for Image Compression
Abstract: We parametrize univariate compactly supported wavelets with 8 and 10 coefficients. We implement them for image compression and search for the best parameters which allow us to compress images. Our result shows there is a parameter which gives us a slightly better compression ratio than the standard 9/7 biorthogonal wavelet for a class of images.
VIGRE Tropical Geometry
2:00pm, Room 304
VIGRE Number Theory
2:30pm, Room 326
VIGRE Algebraic Geometry
3:30pm, Room 323
VIGRE Circle Packing
3:30pm, Room 222
FRIDAY, November 16, 2007
VIGRE Algebra
1:30pm, Room 302
Geometry
2:30pm, Room 410
Speaker: Malcolm Adams, University of Georgia
Title of talk: Problem A6 of the 2006 Putnam Exam, aka Sylvester's Four Point Problem
Abstract: Problem A6 of the 2006 Putnam Exam states "Four points are chosen uniformly and independently at random in the interior of a given circle. Find the probability that they are the vertices of a convex quadrilateral." This is a special case of Sylvester"s four point Problem in which the interior of the circle is replaced by a convex body. I will try to explain the solution to this problem following the n-dimensional solution of J.F.C Kingman. The argument involves a 3 dimensional version of Crofton's second theorem, giving a particularly nice example of Crofton's philosophy that seemingly impossible integrals can sometimes be evaluated by choosing an appropriate coordinate system.