Seminar Schedule
August 27-31, 2007
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.
MONDAY, August 27, 2007
Topology
2:30pm, Room 303
Speaker: Hua Bai, University of Georgia
Title of talk: Kashaev's $6j$-symbols
Abstract: The Kashaev invariants of 3-manifolds are based on 6j-symbols from the representation theory of the Weyl algebra, a Hopf algebra corresponding to the Borel subalgebra of Uq(sl(2,C)). In this talk, we give a brief description of Kashaev’s 6j-symbols, and its connection with the quantum Teichm¨uller spaces theory.
Algebra
2:30pm, Room 410
Speaker: Benjamin Jones, University of Georgia
Title of talk: Chern Classes of Schubert Cells and Varieties: Part 1
Abstract: This is the first of 3 planned talks about singular Chern classes and Schubert
Varieties in the Grassmannian. I will introduce two types of singular Chern classes for general complex algebraic varieties and discuss MacPherson's construction of the functorial Chern-Schwartz-MacPherson class.
Faculty and Graduate Student Social
3:00pm, Room 409
Coffee, Cookies, Tea
TUESDAY, August 28, 2007
VIGRE - Graduate Student Seminar
2:00pm, Room 304
Speaker: Brian Cook, University of Georgia
Title of talk: On the Burr-Erdos Conjecture in Graph Theoretic Ramsey Theory
Abstract: The graph-theoretic version of Ramsey’s Theorem states, in its most simple form, that, for a given graph G, there exists a minimal integer r such that for any partition of the edges of the complete graph K_r=(V_r,E_r), say as E_1 and E_2, we shall have that either G is a subgraph of (V_r,E_1), or a subgraph of (V_r,E_2). For a given graph G, this minimal integer is denoted by r(G). In general, r(G) grows exponentially in |G|, where |G| denotes the number of vertices in G. However, for graphs that are sparse, we should expect that, asymptotically at least, we should be able to do much better. For a particular class of graphs in the ‘more sparse’ genre, a class known as the d-degenerate graphs, Burr and Erdos conjectured that we may improve this bound to a linear one. While the conjecture is still open, there has been much progress made. This talk focuses on some this work, particularly focusing on the partial results for graphs of bounded degree, p-arrangeable graphs, and subdivisions.
WEDNESDAY, August 29, 2007
Faculty and Graduate Student Social
3:00pm, Room 409
Coffee, Cookies, Tea
Algebraic Geometry
3:30pm, Room 410
No Meeting this week
Arithmetic Geometry/Number Theory
3:30pm, Room 304
Speaker: Matthew Smith, University of Georgia
Title of talk: TBA
Mathematical Physics
3:45pm, Room 302
Speaker: Robert Varley, University of Georgia
Title of talk: An introduction to statistical mechanics via the Heisenberg ferromagnet
THURSDAY, August 30, 2007
VIGRE – Algebraic Geometry
2:00pm, Room 323
Organizational Meeting
Applied Math
2:00pm, Room 302
Speaker: Ming-Jun Lai, University of Georgia
Title of talk: Multivariate Splines for Data Fitting and Approximation
Abstract: We explain how to use multivariate splines for scattered data fitting and approximation. Multivariate splines are smooth piecewise polynomial functions over triangulations. For any given set of scattered data, let T be a convenient triangulation of the data locations. We use the minimal energy method, discrete least squares method, penalized least squares method, and L1 spline method to find a fitting or interpolatory spline. We also explain how to deal with the fitting and interpolation when the data set is very large.
VIGRE – Tropical Geometry
2:00pm, Room 304
VIGRE – Circle Packing
3:30pm, Room 222
VIGRE-Number Theory
2:30pm, Room 326
FRIDAY, August 31, 2007
VIGRE-Algebra
1:30pm, Room 302
Geometry
2:30pm, Room 410
Speaker: Jesse Ratzkin, University of Georgia
Title of talk: Rigidiy and deformations of constant mean curvature surfaces
Abstract 1: An a properly embedded, constant mean curvature annulus in 3-space has a definite asymptotic structure, allowing one to assign asymptotic data to each end of a
noncompact, embedded, constant mean curvature. This asymptotes map motivates the following question: how well do the asymptotes determine the constant mean curvature (CMC) surface? For instance, one could ask that a CMC be locally rigid, in that any other
"nearby" CMC must have different asymptotic data. It turns out that one can show local rigidity if the linearized mean curvature operator has certain mapping properties. I will discuss joint work with K. Grosse-Brauckmann, N. Korevaar, R. Kusner, and
J. Sullivan in which we prove the necessary mapping properties for genus zero CMC surfaces contained in a solid slab.
Abstract 2: We continue the previous discussion of local and infinitesimal rigidity of CMC surfaces with some details of the proof of our theorem.