University of Georgia
Department of Mathematics

Seminar Schedule
February 23-27, 2004

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

MONDAY, February 23, 2004

VIGRE - Algebra
2:30p.m., Room 410
Speaker: Markus Hunziker, University of Georgia
Title of talk: The Weyl Character Formula

Topology
2:30p.m., Room 322
Speaker:
Will Kazez, University of Georgia
Title of talk: Bypasses and pinwheels
Abstract: I will describe recent work which describes when adding a bypass to a tight product structure preserves tightness.

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

Lie Theory
3:30p.m., Room 303
Speaker: Jon Kujawa, University of Georgia
Title of talk:
"An Introduction to Crystals, III"
Abstract:
This will be the third (and final) talk on crystal bases. We will spend the majority of our time considering specific examples of crystal graphs and nice combinatorial descriptions of them. Even those who have been unable to attend parts I and II of this series should find the examples interesting and accessible.

Stochastic Processes
3:30p.m., Room 410
Speaker:
Dan Kannan, University of Georgia
Title of talk:
Markov Processes, continuation

TUESDAY, February 24, 2004

VIGRE Graduate Student Seminar
2:00p.m., Room 304
Speaker:
Kevin James, Clemson University
Title of talk:
Sums of Hruwitz class numbers
Abstract: The Hurwitz class number $H(N)$ is defined to be the number of binary quadratic forms of discriminant -N counted with weight 1 except when the form is proportional to $x^2+y^2$ or $x^2+xy+y^2$ when the form is counted with weight 1/2 or 1/3 respectively. For any odd prime $p$, Kummer's Theorem states that

$$ \sum_{|r|<2\sqrt{p}} H(4p-r^2)=2p.$$

We are interested in considering subsums of the above sum of the form

$$ \sum_{\substack{|r|<2\sqrt{p} \\ r\equiv i \pmod{q} }} H(4p-r^2).$$

Since some of these partial sums can be viewed as counting isomorphism classes of elliptic curves over $\mathbb F_p$ with an $\mathbb F_p$-point of order $q$, it is not surprising that these sums exhibit predictable patterns. However, we have also found patterns for several othercases.

In this talk we will demonstrate the computations that lead to formulas analogous to that of Kummer's theorem for these subsums. We will discuss the proofs of the formulas which we can prove and will point out some formulas which seem to hold but which have not yet been proved. (This work was done in the summer of 2003 at Clemson for the ``REU in Computational Number Theory and Combinatorics'' funded by NSF with program participants Brittany Brown and Amy Stout and Tim Flowers)

Special Seminar in Analysis
2:00-4:00p.m., Room 410
Speaker:
Ernie Croot, Georgia Tech
Title of talk: Arithmetic Progressions in Sumsets

Wavelet Analysis
2:00p.m., Room 326
Speaker: Haipeng Liu, University of Georgia
Title of talk: Laurent polynomial matrix extension

WEDNESDAY, February 24, 2004

Berkovich Spaces Seminar
11:00a.m., Room 410
Organizers: Matthew Baker and Robert Rumely

Algebra
2:30p.m., Room 322
Speaker:
Daniel Nakano, University of Georgia
Title of talk:
Les suites spectrales pour l'ingenieur

Algebraic Geometry
2:30p.m., Room 303
Speaker:
Elham Izadi, University of Georgia
Title of talk:
Algebraic geometry and physics - an introduction

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

Numerical Analysis
3:30p.m., Room 303
Speaker: Ming-Jun Lai, University of Georgia
Title of talk: B-spline curves (continued)

Number Theory
3:45p.m., Room 304
Speaker: Robert Rumely, University of Georgia
Title of talk:
TBA


THURSDAY, February 26, 2004

VIGRE - Cardiac Physiology
2:30p.m., Room 304
Speakers:
TBA
Activity:
We will continue our discussion of ion channels in the context of barrier models.

VIGRE - Contact Topology
2:00p.m., Room 410
Organizer: Gordana Matic, University of Georgia

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

Colloquium
3:30p.m., Room 304
Speaker: Brian Parshall, University of Virginia
Title of talk: Tilting modules, categorical equivalences and character formula
Abstract. Tilting modules arise in varous situations in representation theory, from quiver algebras to algebraic groups. We will describe a new category equivalence obtained using tilting theory. A possible application of 1-cohomology of symmetric groups to the representation theory of general linear groups will be indicated, as well as the extension of the methods to other reductive and quantum groups.

Student Number Theory
3:30p.m., Room 303
No Meeting this week

FRIDAY, February 27, 2004

CATS
1:25-2:15pm, Room 306
Speaker: Kaan Tariman, Dept. of Computer Science, University of Georgia
Title of talk: Genetic Algorithms for SCFG Estimation
Abstract: Stochastic context free grammars are used to model RNA secondary structures. Inside-Outside Algorithm (Lari & Young, 1990) estimates the parameters associated with the rules in the grammar with a large time and memory complexity. We introduce genetic algorithms to solve the same problem with its flexibility and simplicity.

Electrodynamics Seminar
2:30p.m., Room 322
Speaker: Robert Varley, University of Georgia
Title of talk: The Dirac equation and the parity operation

Geometry
2:30p.m., Room 326
Speaker: TBA
Title of talk:
TBA