Topic: Lattice point problems and distribution of values of quadratic forms February 1

Presenter: Friedrich Goetze, University of Bielefeld

Topic: TBA February 5

Presenter: Hongkai Zhao, University of California, Irvine

Topic: Elliptic genera of singular varieties February 6

Presenter: A. Libgober, Chicago Circle

Topic: Quantum lattice systems at intermediate temperatures February 7

Presenter: Daniel Ueltschi, Princeton University

Topic: TBA February 9

Presenter: Claude LeBrun, SUNY Stony Brook

Topic: TBA February 12

Presenter: Terry Lyons, University of Oxford

Topic: Jet schemes of locally complete intersection canonical singularities February 13

Presenter: M. Mustata, University of California at Berkeley

Topic: TBA February 13

Presenter: Margarent Wright, Bell Labs

Topic: Capacity of Quantum Channels February 14

Presenter: Mary Beth Ruskai, University of Massachusetts, Lowell

Topic: TBA February 14

Presenter: J. Arthur, University of Toronto and the Institute for Advanced Study

Topic: Variational problems from quantum field theory: February 15

The Chern-Simons-Higgs model

Presenter: Juergen Jost, Max Planck Institute, Leipzig

Topic: TBA February 19

Presenter: Paul Barford, Wisconsin University

Topic: Branched covers of the projective line and the Chow ring of the moduli February 20

space of curves

Presenter: R. Vakil, MIT

Topic: Higher-period ordered phases on the Bethe lattice February 21

Presenter: James Freericks, Georgetown University

Topic: On the smooth ergodic theory of some examples of parabolic flows February 21

Presenter: Giovanni Forni, Princeton University

Date: Wednesday, February 21, 2001, Time: 4:00 p.m., Location: Fine Hall 314

Abstract: We will present recent results on the behaviour of ergodic averages of smooth functions for two examples of `parabolic' conservative flows: generic area-preserving flows (with saddle-like singularities) on higher genus surfaces and horocycle flows on (compact) surfaces of constant negative curvature. We prove that the deviation of ergodic averages from the leading behaviour determined by the ergodic theorem exhibits a power-law decay controlled by invariant distributions. In the case of flows on higher genus surfaces this result was part of a series of conjectures by M.Kontsevich and A.Zorich. The proofs are based on the analysis of the hyperbolicity properties of the appropriate `renormalization' dynamics, related to the Teichmuller flow on the moduli space in the case of flows on higher genus surfaces and to the geodesic flow in the case of horocycle flows.

Topic: TBA February 23

Presenter: Gary Jensen, Washington University in St. Louis

Topic: Stochastic Optimization Problems in Finance February 26

Presenter: Ronnie Sircar, ORFE, Princeton University

Topic: TBA March 5

Presenter: Jan Hesthaven, Brown University

Topic: TBA March 20

Presenter: J. Starr, MIT

Topic: TBA March 26

Presenter: Thomas Liggett, University of California, Los Angeles

Topic: Some mathematical challenges from materials science March 28

Presenter: J. Taylor, Rutgers University

Topic: TBA April 2

Presenter: Eric Vanden-Eijnden, CIMS, New York University