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