November 27 – December 1, 2006
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.
MONDAY, November 27, 2006
Topology
2:30pm, Room 304
Speaker: Gordana Matic, University of Georgia
Title of talk: Contact topology and the invariant of Ozsvath
and Szabo, continued
Joint Algebra and Algebraic Geometry Seminar
12:10pm, Room 208
Speaker: Matt Ondrus, University of Arizona
Title of talk: Whittaker modules for generalized Weyl algebras
Abstract: In 1978, B. Kostant wrote a paper in which he described
the so-called Whittaker modules for a given finite-dimensional semisimple Lie
algebra g. These modules form an important component of the representation theory
of Lie algebras, and analogues of his results have since been given for Weyl
algebras, quantum groups, and other related algebras. Many of these algebras
are in fact examples of a class of algebras known as generalized Weyl algebras.
It is possible to define the notion of a Whittaker module for a generalized
Weyl algebra, and this definition coincides with the classical notion of Whittaker
modules in the above cases. We will discuss ongoing work with G. Benkart aimed
at better understanding Whittaker modules for generalized Weyl algebras.
Joint Algebra and Algebraic Geometry Seminar
2:30pm, Room 410
Speaker: Alexander A. Mikhalev (Moscow University, Fulbright
scholar at CUNY)
Title of talk: Groebner-Shirshov bases for ideals in non-commutative
algebras
Abstract: Groebner bases provide one of the most important
computational tools in commutative algebra and algebraic geometry. For example,
it is the foundation of the widely used program Macaulay for symbolic computations
in algebraic geometry.
Groebner-Shirshov bases generalize Groebner bases to the case of noncommutative
rings. (Historically, they were actually introduced by Shirshov several years
before Buchberger defined Groebner bases!) In this talk, we will introduce the
Groebner-Shirshov bases and explain what is known about them.
We will also outline some applications to non-commutative algebraic geometry.
Faculty and Graduate Student Social
3:00pm, Room 409
Coffee, Cookies, Tea
TUESDAY, November 28 2006
VIGRE
Graduate Student Seminar
2:00pm, Room 302
Speaker: Matthew Ondrus, University of Arizona
Title of talk: Combinatorial Representation Theory of the
Symmetric Group
Abstract: Group theorists are often concerned with understanding
the complex simple modules (i.e., irreducible representations) of a given group.
It is well-known that the simple modules are in one-to-one correspondence with
the conjugacy classes of the group, but it is not always easy to make this correspondence
explicit. In the case of the symmetric group, however, there is a nice combinatorial
rule for constructing the simple module corresponding to a particular conjugacy
class. We will discuss this combinatorial construction and also look at what
happens when the underlying field is changed to be a field of characteristic
p.
Wavelets and Splines
2:30pm, Room 524
Speaker:TBA
Title of talk: TBA
WEDNESDAY, November 29, 2006
Number
Theory/Arithmetic Geometry
2:30pm, Room 410
Speaker: Patrick Corn, University of Georgia
Title of talk: Genus-2 curves and Brauer-Manin obstructions
Abstract: I will attempt to summarize a research project of
van
Luijk and Logan whose goal is to exhibit examples of nontrivial 2-torsion elements
of the Tate-Shafarevich group of the Jacobian of certain genus-2 curves. The
problem is not new, and so far the results may not be either, but the method
is--such nontrivial elements will appear whenever there is a Brauer-Manin obstruction
to rational points on a certain K3 Kummer surface.
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea, Cookies
THURSDAY, November 30, 2006
VIGRE-Algebraic Geometry
2:00pm, Room 410
VIGRE - Quantum Mechanics
3:30pm, Room 410
FRIDAY, December 1, 2006
Geometry
2:30pm, Room 410
Speaker: John McCuan, Georgia Institute of Technology
Title of talk: Minimal graphs with jump discontinuities
Abstract: We construct minimal graphs over smooth annular domains
with jump discontinuities on the inner boundary. This answers a question of
John Urbas. I will also give a brief survey of boundary behavior problems for
solutions of the graphical Plateau problem in the context of Giusti's generalized
solutions. The original result presented in this talk is joint work with Robert
Huff.
VIGRE-Algebra
2:30pm, Room 304