University of Georgia
Department of Mathematics
Seminar Schedule
March 15 - 19, 2004
All Seminars are held in Boyd Graduate Studies Bldg. unless
otherwise noted.
VIGRE - Algebra
2:30p.m., Room 410
Speaker: Daniel Nakano, University of Georgia
Title of talk: Support varieties for Weyl modules
Topology
2:30p.m., Room 322
Speaker: Nathan.Habegger, University of Nantes, France
Title of talk: Some Remarks on the Poincare Conjecture
Abstract: A pseudo-handlebody is a 3-manifold M for which the fundamental
group of the boundary of M surjects onto
the fundamental group of M modulo the intersection of the lower central series.
The Poincare Conjecture can be reformulated in terms of splittings of S^3 into
pseudo-handlebodies. Work of Scharleman-Thompson on Heegard splittings can be
used to further simplify the reformulation. One can also introduce the notion
of the Milnor invariant (higher linking numbers) and give a reformulation in
terms of these.
Faculty and Graduate Social
3:00p.m., Room 409
Coffee, Tea, Cookies
Lie Theory
3:30p.m., Room 303
No Meeting this week
Stochastic Processes
3:30p.m., Room 410
No Meeting this week
VIGRE Graduate Student Seminar
2:00p.m., Room 304
Speaker: Ed Azoff, University of Georgia
Title of talk: Dynamics in [0,1)
Abstract: Let E be an equivalence relation on a set X.
A _uniformization_ of E is a subset of X which meets each equivalence class
determined by E in precisely one point. Finding "nice" uniformizations
is a common mathematical goal. For example, Jordan canonical forms solve the
uniformization problem for the relation of similarity on complex matrices.
After some general remarks, we will specialize to the following setting. Given
a bijection f of the interval [0,1), define x~y if and only if some (forward,
backward, or neutral) iterate of f sends x to y.
We will discuss classical work of Poincare, Denjoy, and Glimm-Effros to the
effect that the resulting equivalence relation is either very good or very bad.
We will also examine some concrete examples illustrating how hard it can be
to decide which alternative holds for a specific f. Along the way, we will catch
glimpses into descriptive set theory (defining what "nice" means),
dynamics (examining limit sets of orbits), and measure theory (a sneaky way
to
show nice uniformizations do not exist).
My interest in this topic arose from joint work with Eugen Ionascu on a question from wavelet theory. If time permits, we will briefly discuss the connection.
Special Seminar in Analysis
2:00-4:00p.m., Ga Tech, Rm 255
Speaker: Jason Metcalfe
Title: Nonlinear wave equations and Strichartz inequalities.
Wavelet Analysis
2:00p.m., Room 326
Speaker: Haipeng Liu, University of Georgia
Title of talk: A Constructive Algorithm for Polynomial
Matrix Extension, continued
Berkovich Spaces Seminar
11:00a.m., Room 410
Organizers: Matthew Baker and Robert Rumely
Algebra
2:30p.m., Room 410
Speaker: Jon Kujawa, University of Georgia
Title of talk: Crystals and the Representation Theory of the Supergroup
GL(m|n)
Abstract: We will discuss the modular representation theory of the
supergroup Gl(m|n). In particular, we will see that important aspects of the
representation theory are controlled by the combinatorics of an explicitly described
crystal graph.
Algebra Geometry Seminar
2:30p.m., Room 303
Speaker: Klaus Hulek, University of Hanover
Title of talk: Small algebraic sets
Abstract: It is well known that an irreducible non-degenerate variety
of minimal degree is either a plane, a quadric hypersurface, a rational normal
scroll, or a cone over a Veronese surface. There is a similar classification,
due to Xambo, for reducible, equi-dimensional algebraic sets connected in codimension
1. We call a (reduced) algebraic set X small if for any plane L which intersects
X in a finite scheme the degree of the intersection of X and L is at most dim
L + 1. This is the right generalization of minimal degree varieties in the non
equi-dimensional case. We prove that X is small if and only if it is 2-regular
and show that every such set can be built from a sequence of linearly joined
minimal degree varieties. This is a report on joint work with
D. Eisenbud, M. Green and S. Popescu.
Faculty and Graduate Social
3:00p.m., Room 409
Coffee, Cookies, Tea
Numerical Analysis
3:30p.m., Room 303
No Meeting this week
Number Theory
3:45p.m., Room 304
Speaker: Eric Brussel, Emory University
Title of talk: Bilinear forms and Galois cohomology
Abstract: Suppose $k$ is a field that contains all roots of
unity. The famous theorem of Merkurjev-Suslin states that the Galois cohomology
group $H^2(G_k,\mu)$ is generated by cup products. We discuss the philosophy
behind this theorem and its generalization, the Bloch-Kato conjecture, recently
claimed by Voevodsky. We show how to use the Merkurjev-Suslin Theorem to compute
a ``behavioral ideal'' for the Brauer group of $k$. We apply similar ideas to
the case where $k$ is a generalized local field, generalizing part of Hasse's
classical theory of the Brauer group of a local field.
VIGRE - Cardiac Physiology
2:30p.m., Room 304
Speakers: TBA
Activity: TBA
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 328
Speaker: Dr. Thomas Grandine, from the Math. Group of the Boeing Company,
Seattle, Washington
Title of talk: Geometry Generation for Analysis and Optimization
Abstract: Preliminary design requires timely engineering analysis of
large numbers of designs. This leads to the requirement that geometric models
be created both rapidly and automatically. Moreover, geometric models so created
must necessarily be part of a continuous parametric family of designs, all of
which satisfy a large number of shape and spatial integration requirements for
the intended vehicle family. Although commercially available geometry systems
have some of the attributes needed to satisfy
geometry generation requirements for preliminary design (e.g. many are parametric),
none are ideally suited for this application. For many years (decades, in fact),
we have been pursuing the holy grail of advanced geometry generation tools which
satisfy both the stated and unstated requirements imposed by preliminary design
of advanced vehicles. This talk will describe the status of our quest as embodied
by the Boeing General Geometry Generator (GGG), our current best effort which
has enjoyed some success in design space exploration and optimization.
Student Number Theory
3:30p.m., Room 303
Speaker: TBA
Title of talk: TBA
CATS
1:25-2:15pm, Room 306
Speaker: TBA
Title of talk: TBA
Electrodynamics Seminar
2:30p.m., Room 322
Speaker: Cal Burgoyne, University of Georgia
Title of talk: Introduction to the quantization of the
Maxwell and Dirac
Geometry
2:30p.m., Room 326
Speaker: John Sullivan, TU Berlin.
Title of talk: Ropelength, cloth, and clasps, or something
else entirely