University of Georgia
Department of Mathematics
Seminar Schedule
January 19 - 23, 2004
All Seminars are held in Boyd Graduate Studies Bldg. unless
otherwise noted.
University Holiday
VIGRE Graduate Student Seminar
2:00p.m., Room 304
Speaker: Jason Cantarella, University of Georgia
Title of talk: What every mathematician should know about
mathematical visualization: a quick overview of how to communicate math effectively
with pictures.
Special Seminar in Analysis
2:00p.m., Room 410
No Meeting this week
Wavelet Analysis
2:00p.m., Room 326
Speaker: Jie Zhou, University of Georgia
Title of talk: Construction of wavelets using dilation
factor > 2, continued
Algebra
2:30p.m., Room 410
Speaker: Graham Matthews, University of Georgia
Title of talk: Computing Generators and Relations for Matrix Algebras
over Finite Fields: Part 1
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: Moment map. Duistermaat-Heckman measure. Tian-Donaldson's
conjecture.
Numerical Analysis
3:30p.m., Room 303
Speaker: Ming-Jun Lai, University of Georgia
Title of talk: How well can you approximate Franke functions
from scattered data?, continued
Number Theory
3:45p.m., Room 304
Speaker: Dino Lorenzini, University of Georgia
Title of talk: Abelian varieties with everywhere good reduction
VIGRE - Cardiac Physiology
2:00p.m., Room 304
Speaker: Cynthia Fort, University of Georgia
Title of talk: Diffusion across membranes
VIGRE - Contact Topology
2:00p.m., Room 410
Organizer: Gordana Matic, University of Georgia
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: Yinglei Song, Graduate student, UGA Computer Science
Dept.
Title of talk: Memory efficient RNA pseudoknot prediction with
stochastic grammar modeling
Abstract: Modeling and predicting RNA secondary structures
with pseudoknots remains an important problem in computational biology. The
Parallel Communicating Grammar System proposed by Cai et al. allows the development
of a full
probabilistic model for sequence prediction and profiling. However, the prediction
algorithm based on this model may only be applied to sequences of less than
100 nucleotides due to its exceptionally large space complexity. A new algorithm
that requires significantly less memory has been developed. Experiments show
that this new algorithm can yield excellent prediction results (with an accuracy
of 86%) on sequences intractable for the original optimal algorithm (up to 204
nucleotides) with reasonable computational resource requirements.
Electrodynamics Seminar
2:30p.m., Room 322
Speaker: Cal Burgoyne, University of Georgia
Title of talk: Various presentations of Maxwell's equations and
an introduction to the Clifford algebra on 3-space
Geometry
2:30p.m., Room 323
Speaker: Joe Fu, University of Georgia
Title of talk: Recursions for the unitary kinematic formula,
part 2.
Special Seminar Numerical Analysis
3:30p.m., Room 304
Speakers:Sergey Konyagin (Moscow State University) and Vladimir Temlyakov
(University of South Carolina)
Title of talk: Convergence of Greedy Approximations for
the trigonometric system.
Abstract: We study the following nonlinear method of approximation
by trigonometric polynomials. For a periodic function $f$ we take as an approximant
a trigonometric polynomial of the form $G_m(f) := \sum_{k \in \Lambda} \hat
f(k) e^{i(k,x)} $, where $\Lambda \subset \Bbb Z$ is a set of cardinality $m$
containing the indices of the $m$ biggest (in absolute value) Fourier coefficients
$\hat f(k)$ of function $f$. Note that $G_m(f)$ gives the best $m$-term approximant
in the $L_2$-norm and, therefore, for each $f\in L_2$, $\|f-G_m(f)\|_2 \to 0$
as $m\to \infty$. It is known from previous results that in the case of $p\neq
2$ the condition $f\in L_p$ does not guarantee the convergence $\|f-G_m(f)\|_p
\to 0$ as $m\to \infty$. We study the following question. What conditions (in
addition to $f\in L_p$) provide the convergence $\|f-G_m(f)\|_p \to 0$ as $m\to
\infty$? We look for conditions of the form $\|G_m(f)-G_{M(m)}\|_p\to 0$ as
$m\to \infty$. Some positive and negative results in this direction will be
discussed in the talk.