Seminar Schedule
April 3-7, 2006
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.
MONDAY, April 3, 2006
VIGRE-Algebraic Geometry
3:30pm, Room 304
Topology/Geometry
2:30pm Room 222
Moved to Friday, April 7, 2006
Algebra
2:30pm, Room 410
Speaker: Brian Boe, University of Georgia
Title of talk: Infinite-dimensional modules which "look"
finite-dimensional.
Abstract: A Kostant module is a simple highest weight module
whose u-cohomology decomposes via a formula like Kostant's famous theorem for
the u-cohomology of a finite-dimensional module. Here u is the nilradical of
a parabolic subalgebra of a complex simple Lie algebra. I will discuss some
equivalent formulations, including one involving geometry of Schubert varieties.
I will describe how certain "standard" Kostant modules are associated
to subdiagrams of the Dynkin diagram.
In a second talk, I will show that, for maximal parabolics in simply-laced
type, all Kostant modules with regular integral highest weights are standard.
I will also give a complete classification of all (singular) Kostant modules
for the parabolics associated to Hermitian symmetric spaces. If time permits,
I will show what can go wrong with singular modules for general maximal parabolics,
and propose an idea for handling these.
Faculty and Graduate Student Social
3:00pm, Room 409
Coffee, Cookies, Tea
TUESDAY, April 4, 2006
VIGRE-Graduate
Student Seminar
2:00p.m., Room 304
Speaker: Emille Davie, University of Georgia
Title of talk: Surface Topology, Geometry, and the Mapping
Class Group
Abstract: Do you believe that since compact surfaces are classified
there is little to be studied? Do you believe that the geometry of all surfaces
is Euclidean? If you do, then this talk will open your eyes to a hyperbolic
universe where "straight" lines are curved, punctures are in a galaxy
far, far away, and the 1-dimensional submanifold is king.
Analysis
2:30pm, Room 302
Speaker: Akos Magyar, University of Georgia
Title of talk: k-point configurations in sets of positive
density, Part I
Abstract: We show that if A is a subset of positive upper density
of the n-dimensional integer lattice, then A contains a "copy" of
any given k-dimensional simplex, as long as n>4k. A copy of a simplex T is
a simplex T'', which is obtained from T via translations, rotations and dilations.
In the first talk, we outline the main elements of the argument without giving
detailed proofs, and then discuss the necessary backgrounds from number theory.
The talk should be accessible to graduate students with basic knowledge of complex
analysis.
WEDNESDAY, April 5, 2006
Geometry in the Curriculum Seminar
1:25pm, Aderhold, Room 111
Speaker: TBA
Title of talk: TBA
Algebraic Geometry
2:30pm, Room 410
Speaker: TBA
Title of talk: TBA
VIGRE- Algebra
2:30pm, Room 303
Speakers: Graduate students
Title of talk: Cohomology in degree p+r
Faculty and Graduate Student Social
3:00pm, Room 409
Coffee, Cookies, Tea
Arithmetic Geometry/Number Theory
3:30pm, Room 304
Speaker: Robert Rumely, University of Georgia
Title of talk: Multi-resultants and the Fekete-Leja Transfinite
Diameter, continued
THURSDAY, April 6, 2006
VIGRE – Feynman Diagrams
2:00pm, Room 326
VIGRE – Cardiac Physiology
2:00pm, Room 640
VIGRE- Zeta Functions
2:15pm, Room 302
VIGRE-Algebraic Geometry
2:00pm, Room 304
Special Geometric Analysis Seminar
3:30pm, Room 304
Speaker: Erich Miersemann, Universität Leipzig
Title: The ascent of liquid on a needle
Abstract: If one inserts a needle into an infinite bath of
liquid, a non-planar rotationally symmetric graph over the domain exterior to
the needle is observed. No nontrivial explicit solutions to the problem are
known.
The speaker discusses a recently obtained asymptotic expansion for the surface
of the liquid which relies on matching of coefficients and the strong nonlinearity
of the equation in various ways. In particular, use of a maximum principle at
infinity which fails for Laplace's equation is used and no growth assumptions
at infinity are required.
FRIDAY, April 7, 2006
Probability Theory
2:30-3:30pm, Room 303
Speaker: Jie Yu, University of Georgia
Title of talk: Kalman filter for Markov processes (cont.)
Topology/Geometry
2:30pm Room 302
Speaker: Stavros Garoufalidis (Georgia Tech)
Title of talk: Asymptotic expansions in Quantum Topology
Abstract: The Jones polynomial of a knot is a quantum invariant
that tightly locks geometric and topological information about knotted curves
in space. According to the philosophy of quantum field theory, certain analytic
limits of the Jones polynomial recover general relativity in 3-dimensions (otherwise
known as riemannian and mostly hyperbolic geometry) or 3-dimensional topology.
In the talk we will discuss various such limits, and survey recent progress
on these difficult analytic and arithmetic questions of knotted objects.
In particular, we will formula a conjecture about the Jones polynomial that
captures not only the volume of the knot, but the whole Borel regulator, and
the Chern-Sinoms invariant, and present experimental evidence to 400 digits
for 12 knots (the biggest one, with 14 crossings).