University of Georgia
Department of Mathematics

Seminar Schedule
September 20 – September 24, 2004

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

MONDAY, September 20, 2004

Algebra
2:30-3:30p.m., Room 410
Speaker: Nathan Geer, Georgia Tech
Title of talk: Quantization of Lie superalgebras.
Abstract: For every semi-simple Lie algebra one can construct the Drinfeld-Jimbo algebra U. This algebra is a deformation Hopf algebra defined by generators and relations. To study the representation theory of U, Drinfeld used the KZ-equations to construct a quasi-Hopf algebra A. He proved that particular categories of modules over the algebras U and A are tensor equivalent. Analogous constructions of the algebras U and A exist for classical Lie superalgebras. However, Drinfeld's proof of the above equivalence of categories does not generalize to Lie superalgebras. In this talk, we will discuss an alternate proof for classical Lie superalgebras. Our proof utilizes the Etingof-Kazhdan quantization of Lie (super)bialgebras. It should be mentioned that the above equivalence is very useful. For example, it has been used in knot theory to relate quantum group invariants and the Kontsevich integral.

Probability Theory
2:45-3:45pm Room 302
Speaker: M. Pemy, University of Georgia
Title of talk: European Options: Derivation and Volatility Smile

Faculty and Graduate Social
3:00 p.m., Room 409
Coffee, Cookies, Tea

VIGRE Algebraic Geometry Group
3:30-4:30pm, Room 304

Topology
3:30-4:30pm, Room 326
Speaker: Ken Baker, University of Georgia
Title of talk: Oszvath-Szabo invariants (continued)

Lie Theory
3:30p.m., Room 303
No Meeting this week


TUESDAY, September 21, 2004

VIGRE Graduate Student Seminar
2:00p.m., Room 304
Speaker: Emille Davie, University of Georgia
Title of talk: Knots in S^3 and Rational 2-Tangles
Abstract: This talk will give an elementary introduction to the study of knots in S^3. We will begin with basic definitions then move towards ways of distinguishing two knots via invariants such as, colorability and the Alexander polynomial. I will also discuss the theory of 2-tangles and their connection to knots, focusing on rational tangles giving rise to rational knots. I will conclude the talk with a demonstration of the Knot Plot software available to interested parties everywhere.

Dynamics on Berkovich Space
3:30-5:30p.m., Room 326
No Meeting this week


WEDNESDAY, September 22, 2004

Algebraic Geometry
2:30-3:45 p.m., Room 410
Speaker: Michael Guy, University of Georgia
Title of talk: Gromov-Witten Invariants and Applications
Abstract: Gromov-Witten Invariants are a rather new idea in algebraic geometry which finds its roots in physics. I will give an introduction to the invariants and explain some of the applications to quantum cohomology and enumerative geometry. This will be an "elementary" talk meant to be a survey of the area as well as pointing out some of the topics of current interest in the field.

VIGRE – Cardiac Physiology
2:30p.m., Room 323

VIGRE – Clifford Algebras
2:30p.m., Room 322

Faculty and Graduate Social
3:00 p.m., Room 409
Coffee, Cookies, Tea

Number Theory
3:45 p.m., Room 304
Speaker: Clayton Petsche, University of Georgia
Title of talk: Mahler Measure and Lehmer's Problem
Abstract: This will be an expository talk on the Mahler measure of polynomials, focusing in particular on one of the outstanding open problems in the subject, posed originally by D.H. Lehmer 71 years ago. I will discuss various attacks on the problem over the years, including recent joint work of myself and J. Vaaler. In next week's seminar I will discuss my work on a different (but somewhat related) topic: the equidistribution of the Galois conjugates of points of small height.

THURSDAY, September 23, 2004

VIGRE - Rational points on curves
2:00p.m., Room 304
Speaker: Clayton Petsche, University of Georgia
Title of talk: Introduction to L-functions of elliptic curves


FRIDAY, September 24, 2004

Student Arithmetic/Algebraic Geometry Seminar
12:20p.m., Room 326
Speaker: Charles Pooh, University of Georgia
Title of talk: Algebraic integers in a given set of points
Abstract: It is well-known that there are infinitely many conjugate sets of algebraic integers on the unit circle and finitely many inside the unit circle. I will present some generalizations of this result.

VIGRE-Algebra
2:30p.m., Room 410
Speaker: Jonathan Kujawa, University of Georgia
Title of talk: Representation theory of the symmetric group I

Spline Analysis
2:30-3:30p.m., Room 303
Speaker: Taytana Sorokina, University of Georgia
Title of talk: Trivariate Spline Macro-Elements
Abstract: Several trivariate macro-elements will be discussed. Mainly, the construction of these elements will be shown.

Geometry
2:30 p.m., Room 323
Speaker: John McCuan, Georgia Tech/U. of Georgia
Title of talk: Geometric expansion of curves and surfaces
Abstract: I will describe work of B. Andrews and M. Feldman in which they produce a family of expanding planar curves that start from a givenconvex curve and expand (in a weak sense to be explained) according to an evolution equation. I will then attempt to describe what is involved inobtaining a similar family of expanding surfaces. Such a construction is an ongoing project.

Wavelet Analysis
3:30-4:30 p.m., Room 303
Speaker: O. Cho, University of Georgia
Title of talk: Riesz-Fejer factization of polynomial Matrices
Abstract: The talk is based on the results in a paper by T.N.T. Goodman. The construction is based on the matrix Riesz-Fejer
factization. When a matrix with polynomial entries is positive definite, such a matrix can be factoried into a product of two matrices with polynomial entries.