University of Georgia
Department of Mathematics

Seminar Schedule
March 19 – March 23, 2007

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

MONDAY, March 19, 2007

Algebra
2:30pm, Room 410
No Meeting this week

Topology Seminar
3:30pm, Room 304
Speaker: Yair Minsky, Yale
Title of talk: Coarse geometry of the mapping class group
Abstract: I will discuss work with Jason Behrstock on the large-scale structure of the mapping class group of a compact surface. Relative-hyperbolicity properties coupled with high-rank subgroups make for an interesting mix, and in particular one can establish Brock-Farb's rank conjecture, stating that the maximal dimension of a quasiflat in the group equals the maximum rank of a free abelian subgroup. If time permits I will discuss ongoing work with Behrstock, Kleiner and Mosher on finer structure of the asymptotic cone and quasi-isometric rigidity properties. Similar results have been independently obtained by U. Hamenstadt.

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

TUESDAY, March 20, 2007

VIGRE-Graduate Student Seminar
2:00pm, Room 304
Speaker: Bret Benesh, Harvard University
Title of talk: Maximal Subgroups of Sym(m) that are Isomorphic to a Symmetric Group
Abstract: When is it possible for a symmetric group (denoted Sym(m)) to have a maximal subgroup that is isomorphic to another symmetric group (say, Sym(n))? One easy case is when m=n+1; for example, Sym(13) has a maximal subgroup that is isomorphic to Sym(12). However, there are other interesting and surprising ways in which this can happen.

This talk will describe exactly when such maximal subgroups occur. Only basic knowledge of group theory will be assumed; if you understand this abstract, you will likely understand the bulk of the lecture.

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

Colloquium
3:30pm, Room 304
Speaker: Yair Minsky, Yale
Title of talk: Curve complexes, surfaces and 3-manifolds
Abstract: A compact oriented surface determines an interesting combinatorial object: The complex whose vertices are homotopy classes of simple loops, and whose simplices are subsets of vertices with disjoint representatives. This finite dimensional, locally infinite complex turns out to be useful in studying the mapping class group of a surface, the Teichmuller space of hyperbolic structures on the surface, and the deformation theory of hyperbolic 3-manifolds. I will give a biased survey of this subject.

WEDNESDAY, March 21, 2007

Algebraic Geometry
2:30pm, Room 410
Speaker: Herbert Lange, Erlangen, Germany
Title of talk: Vector bundles on curves in positive characteristic

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

Number Theory/Arithmetic Geometry
3:30pm, Room 304
Speaker: Pete Clark, University of Georgia
Title of talk: Ramanujan Graphs, Part II: Spectral theory and zeta-functions.

VIGRE – Quantum Mechanics
4:00pm, Room 302

THURSDAY, March 22, 2007

VIGRE – ODE
2:00pm, Room 326

VIGRE – Moduli spaces
2:00pm, Room 304

VIGRE – Geometry
2:00pm, Room 410

FRIDAY, March 23, 2007

Applied Math Seminar
12:20pm-1:10pm, Room 304
Speaker: Qing Zhang, University of Georgia
Title of talk: Trading a mean reverting asset: buy low and sell high
Abstract: This paper is concerned with an optimal trading (buy and sell) rule. The underlying asset price is governed by a mean-reverting model. The objective is to buy and sell the asset so as to maximize the overall return. Slippage cost is imposed on each transaction. The associated HJB equations (variational inequalities) are used to characterize the value functions. It is shown that the solution to the original optimal stopping problem can be obtained by solving two algebraic equations which are much simpler to solve. Sufficient conditions are given in the form of a verification theorem. A numerical example is reported to demonstrate the results.

Geometry
2:30pm, Room 410
Speaker: Joe Fu, University of Georgia
Title of talk: The principal kinematic formula for the unitary group, continued
Abstract: Following the introduction of last week, I will state the precise Principal Kinematic Formula for the unitary group, and give some details of the proof. (I promise to talk about the sl_2 action this time.)

VIGRE–Algebra
3:30pm, Room 304

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