University of Georgia
Department of Mathematics

Seminar Schedule
October 6 - October 10, 2003

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

MONDAY, October 6, 2003

Numerical Analysis
1:30p.m., Room 524
Speaker: Ming-Jun Lai, University of Georgia
Title of talk: Band and Time limiting: from the Slepian theory to the wavelet theory
Abstract: We discuss the approximation of band and time limit functions to signals with finite energy and the connection to the wavelet transform.

Geometry
1:30p.m., Room 410
Speaker: Markus Hunziker, University of Georgia
Title of talk: Geometric constructions--- without a compass
Abstract: I will try to convince you that the role of the compass in geometric constructions is overrated. More precisely, I will demonstrate the following two results.

The first is the Poncelet-Steiner Theorem which states that all constructions using a compass and straightedge can be done using a straightedge alone provided that one circle and its center are given.

The second is a result going back to Diocles and Newton which states that using a Carpenter's square (basically a right angle with two markings) one can construct cube roots, trisect angles, etc.

This talk is rated G (for general audience).

Topology
2:30p.m., Room 323
Speaker: Gordana Matic, University of Georgia
Title of talk: Contact structures and fibered links in 3-manifolds
Abstract: I will talk about a paper of Torisu and the related result of Giroux about existence of special open book decompositions related to contact structures.

VIGRE - Algebra Seminar
2:30p.m., Room 410
Speaker: Daniel Nakano, University of Georgia
Title of talk: We will meet to talk about the computations that were done in the last couple of weeks and ideas to push the project further. Also, I will briefly introduce the idea of the collapse of a partition. This will enable us to calculate nilpotent varieties for the standard representation in types B,C,D.

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

Lie Theory
3:30p.m., Room 303
Speaker: TBA
Title of talk: TBA

TUESDAY, October 7, 2003

VIGRE Graduate Student Seminar
2:00-3:15pm, Room 304
Speaker: Daniel Nakano, University of Georgia
Title of talk: I'm a mathematician seeking a job: A presentation on the academic job market in mathematics
Abstract: In my talk, I will provide basic information about the academic job market in mathematics. We will look at the processes of applying for jobs, interviewing, and negotiating a job offer. I encourage anyone who is applying for jobs this year to attend and also those who will be doing so in the near future.

Analysis
3:30p.m., Room 326
Speaker: Jim Solazzo, University of Georgia
Title of talk: Operator Algebras and Interpolation
Abstract: In this talk we will give an overview of formulas for interpolation on the disk, bidisk, and annulus. We will discuss "computability'' issues concerning these interpolation formulas focusing on what we call "C^*-computable''. Associated
to each interpolation formula is an operator algebra. This will allow us to discuss the "minimal'' C^*-algebra generated by such an operator algebra, when the "minimal'' C^*-algebra acts on a finite dimensional Hilbert space we say an interpolation formula is "C^*-computable''.

WEDNESDAY, October 8, 2003

Group Representation & Cohomology
2:30p.m., Room 410
Speaker: Dave Benson, University of Georgia
Title of talk: "Derived categories and stable module categories, continued"

Algebraic Geometry
2:30pm, Room 303
Speaker: Matthew Baker, University of Georgia
Title of talk: The Manin-Mumford Conjecture Revisited
Abstract: There have been many published proofs of the "Manin-Mumford conjecture", which concerns the intersection of a subvariety X of an abelian (or semiabelian) variety A with the torsion subgroup of A. The first proof was given by Raynaud in the 1980's using difficult scheme-theoretic methods. A striking new proof was given several years ago by Hrushovski, who made heavy use of model theory (a branch of mathematical logic). Since few number theorists and algebraic geometers are comfortable with the language of model theory, it was hard for many people to figure out exactly what Hrushovski had done and how. Recently, Pink and Roessler have adapted Hrushovski's argument to the language of classical algebraic geometry, thereby removing all of the model-theoretic results. I will attempt to explain their beautiful argument.

Faculty and Graduate Social
3:00pm, Room 409
Coffee, Cookies, Tea

Number Theory/Arithmetic Geometry
3:30pm, Room 304
Speaker: Robert Rumely, University of Georgia
Title of talk: The Fekete-Szegö Theorem
Abstract: In this talk I will discuss the Fekete-Szegö Theorem on algebraic curves, which gives a precise numerical criterion for the existence of algebraic points satisfying prescribed geometric and topological constraints. It can only be formulated adelically, that is, taking into account all places of the ground field.

I will illustrate how the theorem can be applied in concrete cases, for example producing algebraic integers $x$ with arbitrarily small height, having the property that $2-x$ is a unit.

THURSDAY, October 9, 2003

VIGRE Quantum Mechanics Seminar
2:00p.m., Room 303
Speaker: Cal Burgoyne, University of Georgia
Title of talk: Two-state quantum systems

VIGRE - Contact Topology
9:00a.m., Room 326

Student Number Theory
3:30p.m., Room 304
No Meeting this week

Special Meeting of all Graduate Students
3:30p.m., Room 304
Speaker: Clint McCrory, University of Georgia
Title of talk: "NSF review of VIGRE"
Abstract: I'll give an overview of the Math Department's VIGRE program and discuss the October 20 meeting of the visiting NSF review panel with our graduate students.


FRIDAY, October 10, 2003

CATS
1:25p.m., Room 306
Speaker: Peter Chu, Computer Science
Title of talk: Data Mining: an Algorithmic Overview
Abstract: In both industry and academic research, data mining has become a very "hot" area. In this talk, several leading algorithms in data mining will be examined in detail. For each algorithm, I will start with assumptions, then present a brief algorithm description, discuss its strengths and weaknesses, and finally point out some current research directions.

Wavelet Analysis
2:30p.m., Room 524
Speaker: Ming-Jun Lai, University of Georgia
Title of talk: Marsden's identity using box spline functions
Abstract: We show how to generate polynomials using box spline functions. The formulas are called Marsden's identity.