University of Georgia
Department of Mathematics

Seminar Schedule
April 2 – April 6, 2007

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

MONDAY, April 2, 2007

Algebra
2:30pm, Room 410
Speaker: Terrell Hodge of Western Michigan University
Title of talk: Some Representation-Theoretic Occurrences of the RSK Algorithm
Abstract: The RSK (Robinson-Schensted-Knuth) algorithm creates creates a neat correspondence between certain matrices and ordered pairs of Young tableaux of the same shape. This talk will survey some geometric and representation-theoretic occurrences of the RSK correspondence and generalizations of it, with appearances by representation theory players such as Schur-Weyl duality, the nullcone of a Lie algebra, Springer's representations, and parabolic category $\mathcal{O}.$

Topology Seminar
2:30pm, Room 304
No meeting this week

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

TUESDAY, April 3, 2007

VIGRE-Graduate Student Seminar
2:00pm, Room 304
Speaker: Adam Speight, Department of Risk Management & Insurance,
Georgia State University
Title of talk: Calibration of Recursive Models in One Shot
Abstract: Formulating and solving well-posed, analytically intractable recursive models
is a major challenge. Large models with many parameters are often given only superficial empirical treatment since most parameter estimation strategies require computing accurate numerical solutions a large number of times, which is often considered infeasible or impractical. I propose a numerical technique for simultaneously solving and calibrating a broad class of recursive models. The technique applies directly to local discretizations of continuous time dynamic programming problems and can be adapted to solve similar recursive models of competitive equilibrium, dynamic contracting, and dynamic games.

The defect correction principle used in Multigrid methods is extended and applied to simultaneously solve, calibrate, and identify the models I consider numerically. By coupling the empirical procedure into the model solver, I show heuristically that for a typical model, the solution, calibrated parameters, and sensitivity to changes in data can be computed at about three to four times the cost of solving the model a single time for a fixed set of parameters provided the model responds smoothly to parameter variations and is fully identified model. For over-identified models, the technique is readily extended to accommodate the Generalized Method of Moments and related techniques based on the Delta method.

I illustrate and evaluate my technique by applying it to an infinite-horizon, continuous-time, portfolio choice problem discretized using finite-difference and Markov Chain approximations. I show how computational and analytical techniques from the Multigrid literature can be adapted to provide guidance for how to properly construct a multilevel algorithm and to predict and diagnose performance.

Calibration, Generalized Method of Moments (GMM), Identification, Discretization, Numerical Analysis, Multigrid Methods, Defect Correction, Numerical Dynamic Programming, Sensitivity Analysis

WEDNESDAY, April 4, 2007

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

Algebraic Geometry
2:30pm, Room 410
No meeting this week

VIGRE – Quantum Mechanics
5:00pm, Room 302
Speaker: David Finkelstein, Georgia Institute of Technology (emeritus)

THURSDAY, April 5, 2007

VIGRE – ODE
2:00pm, Room 326

VIGRE – Geometry
2:00pm, Room 410

Special Number Theory Seminar
3:30 pm, Room 304
Speaker: Alina Carmen Cojocaru, Fields Institute and the University of Illinois at Chicago
Title of talk: TBA
Abstract: TBA

FRIDAY, April 6, 2007

Applied Math Seminar
12:20pm-1:10pm, Room 304
(Pizza at 12:10pm)
Speaker: Ronghua Pan
Title of talk: Darcy's Law and porous medium flow
Abstract: The motion of isentropic flow through porous media can be^M decribed by compressible Euler equtions with frictional damping.^M Time asymptotically, the density is conjectured to satisfy the porous^M media equation and the momentum obeys the classical Darcy's law.^M Previous results are valid for small smooth flow away from vacuum.^M In this talk, we report a proof for all physical flows.^M

Geometry
2:30pm, Room 410
Speaker: Matt Mastin, University of Georgia
Title of talk: Chakerian's diameter inequality for plane curves
Abstract: It is well-known that the diameter of a closed curve is bounded above by half the length of the curve. But the curve that realizes the bound, a double-covered segment, has infinite curvature. What if the curve has an upper bound on its curvature? We prove that in this case the diameter bound can be improved.

VIGRE–Algebra
3:30pm, Room 304

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