University of Georgia
Department of Mathematics
Seminar Schedule
February 6 - February 10, 2006
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.
MONDAY, February 6, 2006
Topology/Geometry
2:30pm, Room 222
Speaker: Will Kazez, University of Georgia
Title of talk: Train tracks, branched surfaces
and laminations
Abstract: I will give an introductory talk leading up to a
description of recent results of Skander Zannad on the existence of laminations
supported by branched surfaces.
Algebra
2:30pm, Room 410
Speaker: Jon Kujawa, UGA
Title: An algebraist does knot theory.
Abstract: Knot invariants are intimately related to representations
of Lie (super)algebras and their quantum groups. One such class of invariants
are called weight systems or Vassiliev invariants. In particular, associated
to each Lie (super)algebra one can construct a universal weight system. We will
discuss some recent work in which we use an explicit calculation in the enveloping
algebra of the Lie superalgebra gl(2|1) to obtain a recurrance relation for
the universal weight system associated to gl(2|1) which allows one to inductively
calculate the invariant. This universal weight system is of particular interest
as it specializes to the Links-Gould invariant.
This talk will not assume any special knowledge of knot theory.
TUESDAY, February 7, 2006
VIGRE-Graduate
Student Seminar
2:00p.m., Room 304
Speaker: Nathan Edington, University of Georgia
Title: Computer Implementations of Five Important Approximations
to Pi
Abstract: We briefly introduce the historically significant
and often surprisingly beautiful approximations to pi of Wallis, Newton, Gregory,
Machin and Ramanujan. We then outline how these approximations were implemented
in MATLAB and MathCAD in order to explore and compare the accuracy and rate
of convergence of each approximation.
John Gosselin® Tea Social
3:00pm, Room 409
Coffee, Cookies, Tea
Colloquium
3:30pm, Room 302
Speaker: Xiaoqiang Wang, University of Minnesota
Title of talk: Phase Field Models and Simulations of Vesicle
Bio-Membranes
Abstract: Recently, we began to systematically model and simulate
the shape deformation of vesicle membranes using a unified energetic variational
phase field method based on the minimization of elastic bending energy with
volume and surface area constraints. Mathematical theory and numerical algorithms
are developed to for the phase field models. Rigorous convergence theories of
the numerical methods are investigated. Many simulations are carried out in
static and dynamic, axis-symmetric and full 3D, one component and multi-component
cases. The new phase field modeling approach has the advantage of avoiding tracking
the free interfaces, and it can easily handle topological changes. Meanwhile,
a series of formulae for retrieving the Euler number of the vesicles have been
given and discussed which may be useful for detection and control purposes.
The 3D codes developed for the equilibrium shape deformations and the deformations
and interactions with fluid fields allow us to conduct extensive computational
studies. Both known and new equilibrium configurations have been discovered
in our numerical simulations. A detailed examination of the energetic bifurcation
landscape has been carried out. We have further studied the effect of the spontaneous
curvature and have conducted simulations of vesicle transformations in fluids.
The further development of the phase field approach for multicomponent vesicles
gives us more tools to understand new and complex phenomena recently being experimentally
studied by biologists.
WEDNESDAY, February 8, 2006
Geometry in the Curriculum
1:25pm, Aderhold Hall, Room 111
Speaker: Thomas Banchoff, University of Georgia
Title of talk: Teaching 3-dimensional geometry
Algebraic Geometry
2:30pm, Room 410
Speaker: Valery Alexeev, University of Georgia
Title of talk: "Complete moduli of branchvarieties".
Abstract: I will present a brand new moduli space providing
an alternative both to Hilbert scheme and to Chow variety. It classifies reduced
varieties with a finite map to a fixed projective variety or scheme. Unlike
the Hilbert scheme, only reduced varieties are used. Unlike the Chow variety,
infinitesimal families are meaningful, in particular this moduli space has a
tangent space. Families of branchvarieties have many more local invariants than
families of subschemes. With some basic invariants fixed, the moduli space is
proper. (Based on a joint work with A.Knutson)
John Gosselin® Tea Social
3:00pm, Room 409
Cookies, Coffee, Tea
Arithmetic Geometry/Number Theory
3:30pm, Room 304
No Meeting this week
VIGRE- Algebra
2:30:pm, Room 303
Speaker: Lenny Chastkofsky, University of Georgia
Title of talk: Cohomology computations and conjectures
THURSDAY, February 9, 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
3:30pm, Room 324
FRIDAY, February 10, 2006
Probability Theory
2:30-3:30pm, Room 303
Speaker: David Prager, University of Georgia
Title of talk: Early Exercise Premiums for American Index
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