Seminar Schedule
October 9 - 13, 2006
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.
MONDAY, October 9, 2006
Topology
2:30pm, Room 304
Speaker: Hua Bai, University of Georgia
Title of talk: "Quantum Teichm\"uller
space", continued
Algebra
2:30pm, Room 410
Speaker: Bobbe Cooper, UGA
Title: Support Varieties of Tilting Modules for p=2
Abstract: As considered in this talk, the tilting modules form
a special class of modules over an algebraic group. Their structure can tell
us something about the representation theory of the group, but they are not
yet well understood. J. E. Humphreys has a conjecture for the support varieties
of the indecomposable tilting modules when the characteristic of the ground
field is large enough (p>h). In this talk, I will present a calculation of
the support varieties of the indecomposable tilting modules over GL_n or SL_n
when p=2. This case is not covered by Humphreys' conjecture, so this represents
an extension of his conjecture.
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Cookies, Tea
TUESDAY, October 10, 2006
VIGRE
Graduate Student Seminar
2:00pm, Room 302
Speaker: David Pitts, University of Nebraska
Title of talk: Topology Meets Operator Algebras
Abstract: A Banach algebra is a complete normed algebra, and
one may consider topological properties of the group of invertible elements
in any unital Banach algebra. For example, is the group of invertible elements
arcwise connected? I will discuss this question for the class of infinite upper
triangular matricies (relative to an orthonormal basis). This algebra can be
viewed as a ``noncommutative analog'' of the Hardy algebra of all bounded analytic
functions on the unit disk. The group of invertibles in the Hardy algebra is
not arcwise connected, yet surpisingly, the question of whether the group of
invertibles in the infinite upper triangular matricies is arcwise connected
remains open.
Analysis
3:30pm, Room 222
Speaker: David Pitts, University of Nebraska, Lincoln
Title of talk: Norming subalgebras and isomorphisms of
operator algebras.
Abstract: An operator algebra is a norm closed subalgebra
of the bounded operators on a Hilbert space. Initially operator algebras were
viewed in the category of Banach algebras (and bounded homomorphisms). However,
operator algebras possess additional structure, arising from matricial norms,
which are natural norms on matrices over the algebra, and this structure, together
with ``completely bounded'' homomorphisms makes the class of operator algebras
into a new (and in some sense larger) category. This viewpoint has become much
more widespread in the past 15-20 years and has found numerous striking applications
in operator theory and operator algebras.
As shown by Pop, Sinclair and Smith, matricial norms on an operator algebra
can sometimes be determined by a ``norming subalgebra.'' I will show how this
idea can be modified using a result of Pisier to produce a technique useful
for determining when when two operator algebras which are isomorphic in the
category of Banach algebras are isomorphic in the category of operator algebras
as well. I will conclude with a couple of applications.
WEDNESDAY, October 11, 2006
Algebraic Geometry
2:30pm, Room 410
Speaker: Elham Izadi, University of Georgia
Title of talk: New correspondences on curves and Prym-Torelli,
II
Abstract: This talk will be independent of the first talk.
I will show how the correspondences are constructed, write the polynomial equations
they satisfy and the combinatorial identities that follow.
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea, Cookies
Arithmetic
Geometry/Number Theory
3:30pm, Room 304
Speaker: Nigel Boston, Univ. of South Carolina
Title of talk: Arboreal Galois representations.
Abstract: The theory of Galois groups acting on p-adic vector
spaces has an analogue where they act on locally finite, rooted trees. This
is developed particularly in the case coming from iteration of a given polynomial.
Joint work with Rafe Jones (U. Wisconsin).
THURSDAY, October 12, 2006
VIGRE-Algebraic Geometry
2:00pm, Room 410
Wavelets and Splines
2:30pm, Room 524
No meeting this week
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea, Cookies
Colloquium
3:30pm, Room 304
Speaker: Weiqiang Wang, University of Virginia
Title of talk: Platonic solids, Hamilton's quaternion,
and Dynkin diagrams
Abstract: We describe some classical algebraic and geometric
connections among the five regular polyhedra, finite subgroups of quaternion,
and Dynkin diagrams. We will then discuss a modern variation of the above themes,
via Hilbert schemes of points and wreath products.
VIGRE - Quantum Mechanics
4:45pm, Room 410
FRIDAY, October 13, 2006
Probability Theory
2:30pm, Room 323
Speaker: Jie Yu, University of Georgia
Title of talk: Piecewise deterministic processes.
Geometry
2:30pm, Room 410
Speaker: Malcolm Adams, University of Georgia
Title of talk: Local Attractors for a Class of Replicator
Equations
Abstract: The replicator equation is a system of ordinary differential
equations on an n-simplex that arise in the study of evolutionary game theory.
I will show how the Poincare'-Hopf theorem can be used to prove that in case
the game matrix has a special form, the replicator system has a unique local
attractor. The application of the Poincare'- Hopf theorem in this case is nonstandard
since the n-simplex has corners. If there is time, I will also discuss a combinatoric
argument that the unique local attractor is a global attractor.
VIGRE-Algebra
2:30pm, Room 304