University of Georgia
Department of Mathematics

Seminar Schedule
September 12 – September 16, 2005

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

MONDAY, September 12, 2005

Topology/Geometry
2:30-4:30pm, Room 303
Speaker: Jason Parsley, University of Georgia
Title of talk: An introduction to Ricci flow
Abstract: For a Riemannian manifold, we describe the Ricci flow, whereby the metric changes based on its Ricci curvature. Hamilton introduced Ricci flow when studying the Poincare conjecture, and it is fundamental in Perelman's proposed proof.

The aim of this talk is far away from Perelman and Poincare; the first part of the talk will introduce Ricci curvature and Ricci flow, provide examples, and describe basic results with the hope of building interest in the subject. After a break, the second part will continue with more results, including if time allows, a description of DeTurck's trick for the short-time existence of Ricci flow. The entire talk will be suitable for graduate students.

Algebra
2:30-3:30pm., Room 410
Speaker: Emilie Wiesner, University of Georgia
Title of talk: The Shapovalov determinant and Translation Functors for the Virasoro Algebra, Day Two.
Abstract: Lie algebras with triangular decomposition generalize finite dimensional simple Lie algebras, and much of the representation theory still works in the more general setting. In particular, we can still define the category of modules $\mathcal{O}$ and obtain a decomposition of this category by blocks. Therefore we can consider translation between blocks (that is, translation functors).

The Virasoro algebra is a concrete example of a Lie algebra with triangular decomposition. In my thesis, I considered translation functors for the Virasoro algebra, using the Shapovalov determinant as my primary tool. On Day One of my talk, I will introduce the Virasoro algebra along with some of its representation theory and try to motivate using the Shapovalov determinant as a useful tool for studying translation functors. On Day Two, I'll talk about some of my results.

Faculty and Graduate Social
3:00pm, Room 409
Coffee, Cookies, Tea

TUESDAY, September 13, 2005

VIGRE-Graduate Student Seminar
2:00p.m., Room 303
Speaker: Chad Mullikin, University of Georgia
Title of talk: TBA

WEDNESDAY, September 14, 2005

Algebraic Geometry
2:30-3:45pm, Room 410
Speaker: TBA
Title of talk: TBA

Faculty and Graduate Social
3:00pm, Room 409
Coffee, Cookies, Tea

Number Theory
3:30p.m., Room 304
Speaker: Patrick Corn, University of Georgia
Title of talk: Del Pezzo surfaces and the Brauer-Manin obstruction, continued.

VIGRE-Algebra
3:00p.m., Room 326
Speaker: Daniel Nakano, University of Georgia
Title of talk: Kostant's theorem

VIGRE Algebraic Geometry Group
3:45 pm in room 303

THURSDAY, September 15, 2005

VIGRE- Mathematical Cardiac Physiology
2:00p.m., Room 410
Speaker: Bree Ettinger, University of Georgia
We will have an overview of our plans for the semester and I will give a talk on the Hodgkin-Huxley Model.

VIGRE group on Feynman diagrams
2:00p.m., room 326

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

Colloquium
3:30pm., Room 304
Speaker: Mike Wolf, Rice University
Title of talk: Minimal Desingularizations of Planes in Space
Abstract: We prove that there is only one way to 'desingularize' the intersection of two planes in space to and obtain a periodic minimal surface as a result. After explaining the statement and its context, with an update on recent progress and challenges in minimal surface theory, we give an overview of the proof of the result. The argument is mostly an exercise in, and an introduction to, the basics of Riemann surface deformation theory: we translate the geometry of the minimal surface in space into a statement about an elementary moduli space of planar domains, and then study how those domains vary and degenerate.

FRIDAY, September 16, 2005

Topology/Geometry Special Talk
2:30p.m., Room 410
Speaker: Mike Wolf , Rice University
Title of talk: Grafting and Pruning Projective Structures on Surfaces
Abstract: A projective structure on a Riemann surface admits both a complex-analytic
description (from its roots in univalent mapping theory) and a synthetic description (from a geometric description by Thurston). We survey some recent work on passing between the two perspectives.

Probability Theory
2:30pm, Room 303
No Meeting this week