University of Georgia
Department of Mathematics

Seminar Schedule
February 19 – February 23, 2007

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

MONDAY, February 19, 2007

Topology
2:30pm, Room 304
Speaker: Ko Honda, University of Southern California
Title of talk: Contact Homology and Open Books.
Abstract: I will talk about the joint work (in progress) with Vincent Colin towards calculating the contact homology of a contact 3-manifold from a compatible open book.

Algebra
2:30pm, Room 410
Speaker: Kenyon Platt, University of Georgia
Title of talk: Semisimple infinitesimal blocks of category \mathcal{O}_S
Abstract: Category \mathcal{O}_S is a generalization of the BGG category \mathcal{O}. Category \mathcal{O}_S decomposes into certain subcategories, called infinitesimal blocks. I will discuss conditions for when an infinitesimal block is semisimple for Lie algebras of types A, B, C, F, and G.

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

TUESDAY, February 20, 2007

VIGRE-Graduate Student Seminar
2:00pm, Room 304
Speaker: Jacob Siehler, Washington & Lee University
Title of talk: Categories with Multiple Monoidal Structures
Abstract: Categories with more than one multiplicative structure can serve as a bridge between algebraic topology and higher-dimensional category theory. We will illustrate the axioms of iterated monoidal categories by means of combinatoric examples involving tableaux shapes; sketch the connection to homotopy theory, and state a structure theorem for categories of operads in iterated monoidal categories.

WEDNESDAY, February 21, 2007

Algebraic Geometry
2:30pm, Room 410
Speaker: David Edwards, University of Georgia
Title of talk: Homotopy Theories of Schemes
Abstract: We survey recent developments in defining homotopy theories of schemes, following Voevodsky and others, and describe some of the applications of having such good homotopy theories. We start by describing homotopy theories for topological spaces and then go on to schemes.

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

Analysis - Number Theory/Arithmetic Geometry
3:30pm, Room 304
Speaker: Konstantin Oskolkov, University of South Carolina
Title of talk: Gauss' sums game played by a Schroedinger particle
Abstract: I will present exact evaluations of complete Gauss' sums, including the reciprocity relations of Genocci and Schaar, and also estimates of the incomplete sums, based on the Green's function for the Cauchy initial value problem for the Schroedinger equation of a free particle.

VIGRE – Quantum Mechanics
4:00pm, Room 302

THURSDAY, February 22, 2007

VIGRE – ODE
2:00pm, Room 326

VIGRE – Moduli spaces
2:00pm, Room 304

VIGRE – Geometry
2:00pm, Room 410

FRIDAY, February 23, 2007

Applied Math Seminar
12:20pm-1:10pm, Room 326
(Pizza at 12:10pm)
Speaker: Alexander Petukhov, University of Georgia
Title of talk: New challenges of Information Theory
Abstract: Mathematical aspects of fundamental problems of Information Theory will be discussed, which became hot topics during last two years. Many leading mathematicians, statisticians, and computer scientists switched to these problems. A very incomplete list of them includes D. Donoho, T. Tao, R. Coifman, I. Daubechies, V. Tarokh, E. Candes. The topics include Compression (and Compessed Sensing as a special case), Transmission in Noisy Channels, and Cryptography for real-valued (or, more generally, metric space) data. Instant applications of these problems are digital broadcasting, mobile telephony, the storage of multimedia data. Those problemes for discrete (finite group) data where solved in the 90's.

We show that all mentioned problems in real-valued data can be reduced to finding sparse solutions of systems of linear equations with rectangular matrices. It is known that in a general setting, the problem has non-polynomial computational complexity. The goal of this talk is to discuss existing sub-optimal methods and possible approaches in finding optimal methods.

Geometry
2:30pm, Room 410
Speaker: John Pardon
Talk title: Convexification of Simple Closed Curves
Abstract: The Carpenter's Rule Conjecture states that every planar polygon can be continuously convexified without any self intersections. Connelly, Demaine, and Rote proved the stronger result that a polygon can be convexified so that the distance between every pair of vertices is increasing. I will give an outline of their proof and show how their result can be extended to rectifiable simple closed curves via a limiting process. I then show how parts of the CDR proof can be modified to apply directly to rectifiable curves, although at present this does not yield a fully continuous (i.e. one which does not rely on approximation by polygons) proof of the theorem for rectifiable curves. In the process, I present a generalization of the Farkas Lemma to Banach spaces and a generalization of the Maxwell-Cremona Theorem.

VIGRE–Algebra
3:30pm, Room 304

VIGRE - Hodge Theoretic questions in Algebraic Geometry
3:30pm, Room 303