Seminar Schedule
February 14- February 18, 2005

All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.

MONDAY, February 14, 2005

Algebra
2:30 – 3:30p.m., Room 410
Speaker: Dan Nakano, University of Georgia
Title of talk: Reductive groups, Frobenius kernels and Finite Chevalley Groups: Representation theory and Cohomology, I
Abstract: The first of two talks. The first talk will be a general overview of known results and open conjectures. The second talk will be on recent work with Z. Lin.

Probability Theory
2:45 - 4:00p.m., Room 222
Speaker: C. Zhuang, University of Georgia
Title of talk: Verification of asymptotic expansion in connection with singular perturbed Markov chains

Faculty and Graduate Social
3:00 p.m., Room 409
Coffee, Cookies, Tea

Lie Theory
3:30-4:30p.m., Room 303
No Meeting this week

Topology
3:30-4:30p.m., Room 326
Speaker: Will Kazez, University of Georgia
Title of talk: Ozsvath-Szabo invariants: Special splittings explained.

CATS
4:40-5:30p.m., Room 306
Speaker: Professor Bob Robinson, Department of Computer Science, University of Georgia
Title of talk: Burnside's Lemma and Counting Connected Unrooted Feynman Diagrams and Map
Abstract: Burnside's Lemma (actually due to Cauchy and Froebenius) is the simple fact that the number of equivalence classes of objects under the action of a permutation group G is the average over G of the number of objects left fixed. We'll start by proving this without assuming any prior knowledge of groups.

TUESDAY, February 15, 2005

VIGRE Graduate Student Seminar
2:00p.m., Room 304
Speaker: Jason Parsley, University of Georgia
Title of talk: Introduction to the Poincare Conjecture
Abstract: In 1904, Poincare conjectured that every compact, simply-connected three-dimensional manifold is homeomorphic to the three-sphere. This problem remained unsolved for almost 100 years. Recently, Perelman posted a couple of papers on the Ricci flow, an equation of manifolds evolving based on their curvature, that implied Poincare's conjecture was true.

In this talk, we will start by defining all relevant terms, then briefly describe the history of the Poincare conjecture and mention analogs in higher dimensions. We touch on Thurston's Geometrization Program, which roughly says that there are exactly eight different types of geometries that are possible for three-dimensional manifolds. If time allows, the last few minutes will be devoted to how Hamilton and Perelman used Riemannian Geometry to attack this problem.

Dynamics on Berkovich Space
3:30-5:30p.m., Room 326
No Meeting this week

WEDNESDAY, February 16, 2005

Spline Analysis
1:30-2:30pm, Room 326
Speaker: V. Baramidze, University of Georgia
Title of talk: Markov's Inequality over Spherical Triangles, continued

Algebraic Geometry
2:30-3:45 p.m., Room 410
Speaker: Joe Rusinko, University of Georgia
Title of talk: Mirror Symmetry and Toric Degenerations of Flag Varieties
Abstract: Mirror Symmetry is a byproduct of the physics of string theory. I will look at Calabi-Yau hypersurfaces in toric varieties and describe the mirror families. Then, following Givental, I will describe mirrors of CY hypersurfaces in varieties G/B of complete flags, using Gonciulea-Lakshmibai toric degenerations of G/B, and also a generalization of this construction to partial flags due to Batyrev et al.

Alexeev and Brion have introduced many new degenerations of flag varieties to toric varieties which are described by what they called "string polytopes". I will discuss the implications of these degenerations to mirrors of CYs in G/B. Finally, I will give an explicit description of the string polytopes which follows from the works of Berenstein-Zelevinsky and Postnikov-Gleizer.

VIGRE – Cardiac Physiology
2:30p.m., Room 640

Faculty and Graduate Social
3:00 p.m., Room 409
Coffee, Cookies, Tea

VIGRE-Algebra
3:30p.m. , Room 303
Organizers: Brian Boe, Daniel Nakano
Title of talk: Formulating conjectures beyond p^2

Number Theory
3:45-5:15pm, Room 304
No Meeting this week

THURSDAY, February 17, 2005

VIGRE – Algebraic Geometry
2:00p.m., Room 304

Student Arithmetic/Algebraic Geometry Seminar
3:30p.m., Room 304
Speaker: TBA
Title of talk: TBA

FRIDAY, February 18, 2005

Geometry
2:30p.m., Room 326
Speaker: Tommaso Pacini, Georgia Tech
Title of talk: Area-minimizing cones in higher codimension and special Lagrangian submanifolds.
Abstract: In 1969, Bombieri-De Giorgi-Giusti discovered the first non-trivial examples of codim.-1 area-minimizing cones in R^n. In 1985, Hardt-Simon showed that any such cone admits smooth, area-minimizing "desingularizations": ie, complete hypersurfaces which are asymptotic to the cone at infinity.

In higher codimension, many examples of area-minimizing cones are known, but there are no general results concerning their desingularization. The goal of the seminar is to present "special Lagrangian" (SL) cones as a possibly fertile subclass in which to investigate this issue. In particular we show that, for SL cones in R^6, certain "soft" geometric obstructions to the desingularization problem vanish.

VIGRE – Clifford Algebras
3:30-4:45p.m. Room 302

Wavelet Analysis
3:30-4:30p.m., Room 322
Speaker: Ming-Jun Lai, University of Georgia
Title of talk: The reversed polynomials (Christoffel-Darboux formula), continued