University of Georgia
Department of Mathematics

Seminar Schedule
October 16 - 20, 2006

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

 

MONDAY, October 16, 2006

Topology
2:30pm, Room 304
Speaker: Gordana Matic, University of Georgia
Title of talk: Contact topology and the invariant of Ozsvath and Szabo

Algebra
2:30pm, Room 410
No Meeting this week

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


TUESDAY, October 17, 2006

VIGRE Graduate Student Seminar
2:00pm, Room 302
Speaker: Alexandra Shlapentokh, East Carolina University
Title of talk: On the non-existence of a general algorithm to determine whether an integer equation f(x_1,...,x_n)=0 has integer solutions (Hilbert's Tenth Problem).
Abstract: At the beginning of the XX century the following question was posed by Hilbert: is there an algorithm that can determine whether an arbitrary polynomial equation in several variables and with integer coefficients has integer solutions? This problem became known as "Hilbert's Tenth Problem". In the early 1970's, Yurii Matiyasevich, building on the work by Martin Davis, Hilary Putnam and Julia Robinson showed that Diophantine sets and computably enumerable sets of integers were the same and thus showed that an algorithm sought by Hilbert did not exist. Matiyasevich's result immediately raised another question which proved to be even more vexing: is there an algorithm as described above but for the solutions in rational numbers? This problem is unsolved to this day. We will discuss the current state of this problem and other problems and conjectures which came out of attempts to solve HTP for rational numbers.

Arithmetic Geometry/Number Theory
3:30pm, Room 304
Speaker: Alexandra Shlapentokh, East Carolina University
Title of talk: Hilbert's Tenth Problem over Number Fields

Analysis
3:30pm, Room 222
Speaker: Ed Azoff, University of Georgia
Title of talk: Descriptive Set Theory in Harmonic Analysis
Abstract: A subset E of the unit circle is called a set of uniqueness if the only trigonmetric series which converges to zero outside of E is the zero series. It has been known for some time that every Lebesgue measurable set of uniqueness has measure zero, but it was only shown in 1986 by Debs and Saint Raymond that all sets of uniqueness are of first category. The proof uses techniques from descriptive set theory, i.e., the study of classes of sets more general than, but closely related to, the class of Borel sets. The seminar is intended to give a self-contained exposition of the relevant concepts in descriptive set theory, and to discuss several of its applications in harmonic analysis.

WEDNESDAY, October 18, 2006

Algebraic Geometry
2:30pm, Room 410
Speaker: Valery Alexeev, University of Georgia
Title of talk: First steps in "higher" Gromov-Witten theory

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

Arithmetic Geometry/Number Theory – Special Seminar
3:30pm, Room 304
Speaker: Sybilla Beckmann-Kazez, University of Georgia
Title of talk: NCTM's New Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics


THURSDAY, October 19, 2006

VIGRE-Algebraic Geometry
2:00pm, Room 410

Wavelets and Splines
2:30pm, Room 524
Speaker: Jie Zhou, University of Georgia
Title of talk: Image Compression using Wavelets
Abstract: This is the continuation of the talk by Dr. Jie Zhou last week. We use orthonormal wavelets of dilation factor q=3 for
image compression. I will demonstrate using MATLAB to show we are able to compress images at ratio 128:1 with excellent recovery.

VIGRE - Quantum Mechanics
5:15pm, Room 410

FRIDAY, October 20, 2006

Probability Theory
2:30pm, Room 323
Speaker: Jie Yu, University of Georgia
Title of talk: Piecewise deterministic processes (cont.)

Geometry
2:30pm, Room 410
Speaker: Malcolm Adams, University of Georgia
Title of talk: Local Attractors for a Class of Replicator Equations (continued)

VIGRE-Algebra
2:30pm, Room 304