University of Georgia
Department of Mathematics
Seminar Schedule
January 12 - 16, 2004
All Seminars are held in Boyd Graduate Studies Bldg. unless
otherwise noted.
Topology
2:30p.m., Room 322
Speaker: TBA
Title of talk: TBA
VIGRE - Algebra
2:30p.m., Room 410
Organizer: Dan Nakano, University of Georgia
Activity: We will review some of the previous computations
from last semester and discuss our new computer program to calculate nilpotent
varieties.
Faculty and Graduate Social
3:00p.m., Room 409
Coffee, Cookies, Tea
Stochastic Processes
3:30p.m., Room 410
Speaker: Dan Kannan, University of Georgia
Title of talk: "Kolmogorov's construction of stochastic
processes."
Lie Theory
3:30p.m., Room 303
Speaker:
Title of talk:
VIGRE Graduate Student Seminar
2:00p.m., Room 304
Speakers: Jerry Hower, Mukul Patel, Charles Pooh, and Chao Zhuang
Title of talk: The quantum-mechanical derivation of the
periodic table
Abstract: We will survey how the mathematics of the Schroedinger
equation leads to the quantum numbers (n,l,m) for an electron in an atom. The
Laplace operator, separation of variables, and the ODEs for Laguerre, Legendre,
and exponential functions are involved in this analysis. Then, with the help
of Pauli's exclusion principle, we will show how to construct the periodic table
of the elements.
Special Seminar in Analysis
2:00p.m. at Georgia Tech, Skilles, Rm 108
Speaker: Akos Magyar, University of Georgia
Title of talk: After some organizational discussion, I'll start it,
telling a paper of Bourgain and related questions.
Wavelet Analysis
2:00p.m., Room 326
Speaker: Jie Zhou, University of Georgia
Title of talk: Construction of wavelets using dilation
factor > 2.
Algebra
2:30p.m., Room 410
Speaker: Dave Hemmer, University of Toledo
Title of talk: A row removal theorem for the Ext^1 quiver of symmetric
groups and Schur algebras.
Abstract: In 1981 James proved two theorems about the decomposition
matrices of Schur algebras involving the removal of the first row or column
from a Young diagram. He established corresponding results for the symmetric
group using the Schur functor. We apply James' techniques to prove that row
removal induces an injection on the corresponding Ext1 between simple modules
for the Schur algebra. We then give a new proof of James' symmetric group result
for partitions with first part less than p. This proof lets us demonstrate that
first row removal induces an injection on Ext1 spaces between these simple modules
for the symmetric group. We conjecture our theorem holds for arbitrary partitions.
This conjecture implies the Kleshchev-Martin conjecture that Ext^1(S,S)=0 for
any simple module S in characteristic p>2. The proof makes use of an interesting
fixed-point functor about which little is known.
Faculty and Graduate Social
3:00p.m., Room 409
Coffee, Cookies, Tea
Algebraic Geometry
2:30p.m., Room 303
Speaker: Valery Alexeev, University of Georgia
Title of talk: GIT stability of algebraic varieties and Kahler-Einstein
metrics
Abstract: The talk is going to be half-and-half differential-and-algebraic
geometry. I will introduce a conjecture of Tian and Donaldson relating GIT stability
of algebraic varieties to the existence of metrics of constant scalar curvature.
I will also explain a recent progress made by Donaldson (J. Diff. Geom. 62 (2002),
289-349, based on earlier work of Guillemin and Abreu) in the case of toric
varieties and by the author and Katzarkov (GAFA, to appear) in the case of reductive
varieties. Additional topics to be covered: moment map, Duistermaat-Heckman-Archimedes
measure.
Number Theory
3:45p.m., Room 304
Speaker: Matt Baker, University of Georgia
Title of talk: Canonical heights on abelian varieties over
abelian extensions
Abstract: We will discuss the following result (joint work
with Joe Silverman): Let A be an abelian variety defined over a number field
K, and consider the canonical height function on A attached to a symmetric ample
line bundle L. Then there is a positive lower bound C for the canonical height
of non-torsion points on A defined over the maximal abelian extension of K.
We will also discuss an analogue of this result for the multiplicative group
which was proved earlier by Amoroso, Dvornicich, and
Zannier.
VIGRE - Cardiac Physiology
2:00p.m., Room 304
Speaker: Andrew Sornborger, University of Georgia
Title of talk: More on the Law of Mass Action and Enzyme
Kinetics
Abstract: This week I will review last week's introduction
and finish the discussion of how to model biochemical reactions with differential
equations.
Student Number Theory
3:30p.m., Room 303
Speaker: Nausheen Lotia, University of Georgia
Title of talk: RSA encryption: Do we need strong primes?
Abstract: I willl be talking about whether or not 'strong'
primes are needed to protect against factoring attacks in the RSA cryptosystem.
I will start by quickly going over RSA, and defining what a 'strong' prime is,
and then move onto pollard's p-1 method for factoring which was one of the justifications
for using strong primes. I will then just talk about a couple of other factoring
methods and conclude with whether or not strong primes really are needed or
not.
CATS
1:25-2:15pm, Room 306
Speaker: TBA
Title of talk: TBA
Geometry
1:30p.m., Room 410
Speaker: Joe Fu, University of Georgia
Title of talk: Recursions for the unitary kinematic formula
Electrodynamics Seminar
2:30p.m., Room 322
Speaker: Cal Burgoyne and Robert Varley, organizers
Title of talk: Organizational meeting
Numerical Analysis
3:30p.m., Room 304
Speaker: Ming-Jun Lai, University of Georgia
Title of talk: How well can you approximate Franke functions
from scattered data?