University of Georgia
Department of Mathematics

Seminar Schedule
October 27 - October 31, 2003

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

MONDAY, October 27, 2003

Numerical Analysis
1:30p.m., Room 524
Speaker: Ming-Jun Lai, University of Georgia
Title of talk: Domain decomposition technique for scattered data interpolation (Cont.)

Geometry
1:30p.m., Room 410
Speaker: Jason Cantarella, University of Georgia
Title of talk: The Square Peg Problem
Abstract: It is commonly asserted that one cannot fit a square peg into a round hole. However, it is known that any closed (Jordan) plane curve, it is known that four points on the curve form a rectangle. Therefore, one can fit a rectangular peg perfectly into a hole of any convex shape. Is the same true for square pegs? The talk will cover the (classical) proof for the rectangular peg theorem, and sketch a new approach to the square peg theorem.

Topology
2:30p.m., Room 322
Speaker: Will Kazez, University of Georgia
Title of talk: Lens space surgeries
Abstract: I'll discuss some recent work of Kronheimer, Mrowka, Ozsvath, and Szabo with a focus on how it is applied to knot theory.

VIGRE - Algebra Seminar
2:30p.m., Room 410
Speaker: Brian Boe, University of Georgia
Title of talk: Nilpotent varieties for the adjoint representations of classical Lie algebras via tensor products, continued.

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

Lie Theory
3:30p.m., Room 303
Speaker: Bill Graham, University of Georgia
Title of talk: The Springer resolution and nilpotent orbit covers
Abstract: The Springer resolution of the nullcone plays an important role in the representation theory of Lie groups and Weyl groups. In this talk I will discuss an analogue of this where the principal nilpotent orbit is replaced by its universal cover

TUESDAY, October 28, 2003

VIGRE Graduate Student Seminar
2:00-3:15pm, Room 304
Speaker:Qing Zhang, University of Georgia
Title of talk: An optimal selling rule with regime switching
Abstract: Hybrid (regime switching) control and filtering has been used in various applications for dealing with complex (usually highly nonlinear) dynamic systems. In this talk, I present an application of hybrid models in finance: liquadation of stocks. In particular, a selling rule with two threshold levels - a target price and a stop-loss limit is considered. Optimal threshold levels are obtained by solving a set of two-point boundary value differential equations.

Analysis
3:30p.m., Room 326
Speaker: TBA
Title of talk: TBA

WEDNESDAY, October 29, 2003

Group Representation & Cohomology
2:30p.m., Room 410
No Meeting this week

Algebraic Geometry
2:30pm, Room 303
Speaker: Vyacheslav V. Shokurov (Johns Hopkins University)
Title of talk: Discrepancies and termination of flips
Abstract. Termination of flips and, more generally, of log and of quasi-log flips follows from two expected properties of the minimal discrepancy (md) function on algebraic varieties:

1. semicontinuity of md's on any fixed variety, and
2. ascending chain condition (acc) of md's on varieties of given
dimension.

This reduces the global statement on termination to two local ones. All known proofs of termination follow from this reduction. In particular, this gives the log termination in dimension 3, the special and canonical termination up to dimension 4.

To prove log termination in dimension 4, one only needs the acc in dimension 4 for the md values in the interval [-1,0].

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

Number Theory/Arithmetic Geometry
3:45pm, Room 304 **Note permanent time change**
Speaker: Matt Baker, University of Georgia
Title of talk: Salem numbers, Part II
Abstract: I will discuss a recent construction due to McKee and Smyth of infinite families of Salem numbers.

THURSDAY, October 30, 2003

Fall Break - Student Holiday

FRIDAY, October 31, 2003

Fall Break - Student Holiday