University of Georgia
Department of Mathematics
Seminar Schedule
February 23-27, 2004
All Seminars are held in Boyd Graduate Studies Bldg. unless
otherwise noted.
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
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
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
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
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