University of Georgia
Department of Mathematics
Seminar Schedule
February 16-20, 2004
All Seminars are held in Boyd Graduate Studies Bldg. unless
otherwise noted.
VIGRE - Algebra
2:30p.m., Room 410
Organizer: Daniel Nakano, University of Georgia
Activity: We will compute nilpotent varieties for E_7 and E_8
for bad primes.
Topology
2:30p.m., Room 322
Speaker: Margaret Symington, Georgia Tech
Title of talk: Lefschetz fibers in integrable systems
Abstract: An integrable system induces a singular Lagrangian
fibration on a symplectic manifold. We assume the fibers are compact. Then the
Lagrangian condition forces generic fibers to be tori. If the symplectic manifold
has dimension four then a typical isolated singular fiber of top dimension is
a Lefschetz fiber -- a sphere with one transverse self-intersection. Such fibers
appear with positive self-intersection in physical integrable systems (such
as the spherical pendulum) and in almost toric fibrations (e.g. of the K3 surface).
After discussing some features of the neighborhood of such a fiber I will prove
that a Lefschetz fiber with negative self-intersection cannot occur.
Faculty and Graduate Social
3:00p.m., Room 409
Coffee, Tea, Cookies
Colloquium
3:30p.m., Room 304
Speaker: Prof. Nira Dyn, School of Mathematics, Tel Aviv University
Title of talk: Spline Subdivision Schemes for Compact Sets
Abstract: Motivated by the problem of the reconstruction of
3D objects from their 2D cross sections, we consider spline subdivision schemes
operating on data consisting of compact sets. A spline subdivision scheme generates
from such initial data a sequence of set-valued functions, with compact sets
as images, which converges to a limit set-valued function. In the case of 2D
sets, the limit set valued function, with 2D sets as images, describes a 3D
object. For the case of data consisting of convex sets, we replace addition
by Minkowski sums of sets. Then the spline subdivision schemes generate limit
set-valued functions which can be expressed as linear combinations of integer
shifts of a B-spline, with the initial sets as coefficients. We obtain an O(h^2)
rate of approximation by the limit function, under mild smoothness assumptions
on the set-valued function, from which the initial data is sampled. For the
case of non-convex sets we show that the limit of the spline subdivision schemes,
using the Minkowski sums, is too large to be a good approximation. To define
spline subdivision schemes for general compact sets, we use the representation
of spline subdivision schemes in terms of repeated averages, and replace the
usual average by a binary operation between two compact sets, termed the "metric
average". These schemes are shown to converge in the Hausdorff metric,
and provide an O(h) rate of approximation. The results presented here were obtained
in collaboration with E. Farkhi.
Lie Theory
3:30p.m., Room 303
No Meeting this week
Stochastic Processes
3:30p.m., Room 410
Speaker: Dan Kannan, University of Georgia
Title of talk: Markov Processes
VIGRE Graduate Student Seminar
2:00p.m., Room 304
Speaker: Laura DeMarco, University of Chicago
Title of talk: Polynomial dynamics and potential theory
Abstract: We discuss basic connections between polynomial
dynamics and potential theory in the complex plane. We hope to
describe some of the challenging open problems in the field today. This lecture
should be accessible to all graduate students.
Special Seminar in Analysis
2:00-4:00p.m., Room 410
No Meeting this week
Wavelet Analysis
2:00p.m., Room 326
Speaker: Ming-Jun Lai, University of Georgia
Titleof talk: Compactly supported orthonormal scaling functions
and wavelets in Sobolev spaces
Abstract: We discuss a new density condition which enables
us to construct compactly supported scaling functions in Sobolev spaces in the
univariate setting. Compactly supported wavelets follow naturally.
Berkovich Spaces Seminar
11:00a.m., Room 410
Organizers: Matthew Baker and Robert Rumely
Algebra
2:30p.m., Room 322
Speaker: Jon Carlson, University of Georgia
Title of talk: Crash-course on spectral sequences continued...
Algebraic Geometry
2:30p.m., Room 303
Speaker: Bill Rulla, University of Georgia
Title of talk: Examples Relating to Green's Conjecture
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
Abstract: We continue to discuss how to build B-spline curves
based on nonuniform knot sequences.
Number Theory
3:45p.m., Room 304
Speaker: Matt Baker, University of Georgia
Title of talk: Adelic dynamics of iterated rational functions,
Part II
VIGRE - Cardiac Physiology
2:30p.m., Room 304
Speakers: Andrew Sornborger/Tremaine Skeen, University of Georgia
Activity: This week, we will begin discussing ion channels. These are
the most important components of membranes that we have encountered so far.
Andrew will discuss a particular ion channel model and Tremaine will present
results from a simulation of the model.
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: Prof. Adam Koranyi, City University of New York
Title of talk: Quasiconformal Maps In Several Complex Variables
Abstract: There is no Riemann mapping theorem in C^n for n>1.
But maybe there is such a theorem if we allow quasiconformal (in the following:
qc) maps? (Qc means that the distortion of small spheres is uniformly bounded.)
As it will be explained, one has to consider the Bergman metric of the domains.
The natural candidates for "Riemann maps" are the maps that are qc
with respect to the real part of this metric and preserve its imaginary part
("symplectic qc maps"). There are a number of results, mostly joint
with H. M. Reimann, in the direction of this conjecture. The boundaries of the
domains also have an intrinsic metric which is highly non-isotropic and is defined
with the aid of the Levi form. The main technique is to find qc maps of the
boundaries onto each other that are qc with respect to this metric and then
try to extend them to the interior as symplectic qc maps.
Student Number Theory
3:30p.m., Room 303
No Meeting this week
CATS
1:25-2:15pm, Room 306
Speaker: Angela Maduko, Graduate Student,
UGA Computer Science Dept.
Title of talk: EXACT TSP is DP-Complete
Abstract: To show that EXACT TSP is DP-Complete, we will
first introduce and establish the DP-completeness of the language SAT-UNSAT,
then obtain a reduction from SAT-UNSAT to EXACT TSP.
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 Equation(s)
Geometry
2:30p.m., Room 326
Speaker: TBA
Title of talk: TBA