University of Georgia
Department of Mathematics
Seminar Schedule
January 26 - 30, 2004
All Seminars are held in Boyd Graduate Studies Bldg. unless
otherwise noted.
VIGRE - Algebra
2:30p.m., Room 410
Speaker: Brian Boe, University of Georgia
Title of talk: Nilpotent orbits for classical groups in
characteristic 2
Topology
2:30p.m., Room 322
Speaker: TBA
Title of talk: TBA
Lie Theory
3:30p.m., Room 303
Speaker: Eric Sommers, University of Massachusetts
Title of talk: Normality of nilpotent varieties
Abstract: The talk discusses the question of which nilpotent
varieties in a simple Lie algebra are normal. After reviewing the current status
of the problem, we describe recent progress which resolves the last few cases
in the classical groups.
Stochastic Processes
3:30p.m., Room 410
Speaker: Dan Kannan, University of Georgia
Title of talk: Weak Convergence of Measures
VIGRE Graduate Student Seminar
2:00p.m., Room 304
Speaker: Alexander Petukhov, University of Georgia
Title of talk: Challenging problems of applied Information Theory.
Abstract: I am going to talk about general mathematical principles
of encoding information for compact storage and transmission through lossy channels.
The classical theory of Error Correcting Codes relies on the notion of Shannon's entropy as a measure of the amount of information and on the convolutional technique (in particular, on the theory of algebraic polynomial over Galois fields) as a tool for optimizing the usage of the channel capacity. In his celebrated paper (1948), C. Shannon gave the mathematical foundations of Information theory. In particular, he found theoretical bounds for an amount of information which can be transmitted through a channel and proved the existence of optimal algorithms. However, practically implementable near optimal encoding strategy (so-called, Turbo Codes) was found only in 1993.
Shannon's entropy is an attribute of probability spaces. The success of transmission of the element of probability space means that exactly the same element was decoded. The transmission fails if a wrong element was received after decoding.
In modern systems of telecommunications, the role of multimedia content (audio, video, images, and so on) increases. Such bitstreams should be considered as sequences of integer numbers rather than separate bits. It is clear intuitively that the degree of the protection of bits with different significance has to be different whereas the classical methods provide equal protection. The methods of Error Correcting Codes providing the protection of integer information or, more general, data from (probabilistic) metric spaces and the role of Kolmogorov's entropy (or its combination with Shannons's) will be discussed.
Some demos of Error Correcting Algorithms for the protection of images will be shown.
Special Seminar in Analysis
2:00-4:00p.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 symmetric wavelets of dilation
d>2.
Berkovich Spaces Seminar
11:00a.m., Room 527B
Organizers: Matthew Baker and Robert Rumely
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 II
Faculty and Graduate Social
3:00p.m., Room 409
Coffee, Cookies, Tea
Algebraic Geometry
2:30p.m., Room 303
Speaker: Osamu Fujino, IAS Princeton and Nagoya University
Title of talk: On termination of 4-fold semi-stable log flips
Abstract: A flip is an important surgery operation in algebraic geometry.
The flip conjecture II says there are no infinite sequences of (log) flips.
We treat it in dimension four. More precisely, we explain that every sequence
of four-dimensional semi-stable log flips must terminate.
Numerical Analysis
3:30p.m., Room 303
Speaker: Bree Ettinger, University of Georgia
Title of talk: Experiment of spline approximation of Franke
function.
Number Theory
3:45p.m., Room 304
Speaker: Eric Pine, University of Georgia
Title of talk: Bounding Taxicab Numbers
Abstract: Taxicab numbers are integers which can be expressed
as the sum of cubes of two integers in two distinct ways. I'll discuss ways
of counting such integers, and describe some of the previous and current upper
and lower bounds on these counts. Included will be work by Hooley, Wooley, and
Heath-Brown.
VIGRE - Cardiac Physiology
2:00p.m., Room 304
Speaker: Bree Ettinger, University of Georgia
Activity : This week we will be working together to get a simulation
of mediated glucose transport running. Bree will be
providing us with some guidance and Maple code.
VIGRE - Contact Topology
2:00p.m., Room 410
Organizer: Gordana Matic, University of Georgia
Student Number Theory
3:30p.m., Room 303
No Meeting this week
CATS
1:25-2:15pm, Room 306
Speaker: Rod Canfield, Univeristy of Georgia, Dept. of Computer
Science
Title of talk: Space Complexity of Path-finding in Graphs
Abstract: The problem is to find out if it is possible to travel from
one prescribed vertex to another in a graph when one is severely limited in
memory. Our emphasis will be to explain some of the essential ideas in two recent
advances on this problem, [Nisan, Szemeredi, Wigderson: citeseer.nj.nec.com/233520.html]
and [Armoni, Ta-Shma, Widgerson, Zhou : JACM 47]
Electrodynamics Seminar
2:30p.m., Room 322
Speaker: Cal Burgoyne, University of Georgia
Title of talk: Clifford Algebra in Minkowski 4-space and Maxwell's
eEquation(s)
Geometry
2:30p.m., Room 326
Speaker: TBA
Title of talk: TBA