## 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 hypergraph 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

determined by considering factorizations of the particular function which
determines the

hyperspace. In the first talk we will discuss the necessary background to follow
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.