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MATHEMATICS SEMINAR SCHEDULE

MONDAY, September 9, 2002

Group Representation & Cohomology

2:30pm, Room 410
Speaker: Graham Matthews, University of Georgia
Title of talk: “On the Indecomposable Representations of a Finite Group, by J.A. Green”

Topology
2:30 p.m., Room 326
Speaker: Gordana Matic, University of Georgia
Title of talk: An introduction to Ozsvath-Szabo invariants of 3-manifolds, continued

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

Numerical Analysis
3:30 p.m., Room 410
No Meeting today. Please see Wednesday, Sept. 11, 2002

Analysis
3:30 p.m., Room 222
No Meeting today. Please see Tuesday, Sept. 10, 2002

Cats
4:40 p.m., Room 306
Speaker: Aaron Windsor, Graduate Student, Computer Science Dept.
Title of talk: “Maximal Independent Sets in Hypergraphs”
Abstract: A hyper graph is a generalization of a graph where arbitrarily many vertices
may appear in a single edge. A maximal independent set (MIS) in a hypergraph is a
subset of the vertex set that doesn't induce any edges and cannot be enlarged by adding
more vertices. There's a simple greedy algorithm for this problem that's sequential in
nature, but it is a difficult algorithm to parallelize efficiently. We'll discuss some recent
work on this problem regarding hypergraphs with given degree bounds on the vertices.

TUESDAY, September 10, 2002

VIGRE
2:00 p.m-3:15 p.m., Room 304
Speaker: Matthew Baker, University of Georgia
Title of talk: “April Fools, Elliptic Curves, and Complex Multiplication”
Abstract: In the April 1975 issue of Scientific American, Martin Gardner wrote that a
mathematician at University of Arizona had proved that exp(pi*sqrt(163)) is an integer.
The article was a hoax, but in fact this number is surprisingly close to an integer (check it
out for yourself!), and there is a good theoretical reason why this should be so. In the
course of explaining this last assertion, we will touch on some of the most important
topics in modern number theory, including elliptic curves, modular functions, complex
multiplication, and class numbers.

Algebraic Geometry
3:30 p.m., Room 326
Speaker: Ivan Cheltsov, University of Georgia
Title of talk: “Birationally rigid hypersurfaces”, Part II
Abstract: In the second part of my talk "Birationally rigid hypersurfaces" about the
recent paper of Alexander Pukhlikov  I will explain the proof of its main technical
result - points on hypersurface X of degree N in N-dimensional projective space
could not be centers of canonical singularities of any "movable" log pairs
on X with numrically trivial log canonical divisor . I will briefly
remind why this result implies the birational rigidity of X (the best written source about
the link between the birational rigidity and singularities of "movable" log pair (variety
and linear system multiplied by some positive rational number) is

Student Number Theory
3:30 p.m., Room 303
Speaker: Xander Faber, University of Georgia
Title of talk: A topic near and dear to my heart ... one of the holy grails of number theory.
Abstract:
I don't want to give away the secret, but this will be a talk accessible to any
graduate student who has seen modular arithmetic at some point (manipulating
congruences).

Analysis
3:30 p.m., Room 222
Speaker: Jim Solazzo, University of Georgia
Title of talk: “Hankel Operators, Reflexivity, and Factorization”
Abstract: This will be a series of two talks, discussing the joint work of E. Azoff, R.
Martinez, and J. Solazzo. The first talk will be given by Jim Solazzo and the second talk
will be given by Ed Azoff. In these talks we will give necessary and sufficient conditions
in order for a hyperspace of Hankel operators to be reflexive. These conditions are
de termined by considering factorizations of the particular function which determines the
hyperspace. In the first talk we will discuss the necessary background to fol low the talks
and our results in the finite-dimensional setting. The second talk will focus on our results
in the infinite-dimensional setting.

WEDNESDAY, September 11, 2002

Wavelet Analysis
10:10 – 11:00 a.m., Room 410
Speaker: Haipeng Liu, University of Georgia
Title of talk: “Biorthogonal Wavelets in Sobolev Spaces”
Abstract: We finally summarize up the discussions on biorthogonal wavelets in Sobolev spaces.

Graduate Teaching Seminar
2:30 p.m., Room 303
Speaker: Sybilla Beckmann-Kazez, University of Georgia
Title of talk: “Writing on Teaching”

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

Lie Theory
3:30 p.m., Room 302
Speaker: Bill Graham, University of Georgia
Title of talk: “A lookup conjecture for rational smoothness”
Abstract: Determining which points of a Schubert variety are rationally smooth (i.e.,
points at which the Schubert variety is a rational homology manifold) is important in
representation theory. Although methods exist for determining whether a point is
rationally smooth, they are combinatorially complicated . In this talk (which is on joint
work with Brian Boe) I will discuss a conjecture which would greatly simplify testing for
rational smoothness, along with proofs in special cases.

Number Theory
3:30 p.m., Room 304
Speaker: Dino Lorenzini, University of Georgia
Title of talk:Reduction of Curves of Genus 1”

Numerical Analysis
3:30pm, Room 410
Speaker: Ming-Jun Lai, University of Georgia
Title of talk: “Iterative Methods by Subspace Correction”

FRIDAY, September 13, 2002

Geometry
2:30 p.m., Room 322
Speaker: Nancy Wrinkle, University of Georgia
Title of talk: “The simple clasp”
Abstract: I will discuss candidates for ropelength critical configurations of the simple
clasp. This is work in progress with Jason Cantarella, Joe Fu, John Sullivan, and Rob
Kusner.

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