As of May 2 - May 4, 2001

Special Analysis Seminar  ***
Topic:  On the regularity of solutions to the 2D-modified Navier-Stokes system
Presenter: Tim Shilkin, Steklov Institute, St-Petersburg
Date: Wednesday, May 2, 2001, Time: 3:00 p.m., Location: Fine Hall 314

Special Analysis Seminar  ***
Topic: A cheap Caffarelli-Kohn-Nirenberg inequality for Navier-Stokes equations with hyper-dissipation
Presenter: Natasa Pavlovic, University of Illinois, Chicago
Date: Wednesday, May 2, 2001, Time: 4:00 p.m., Location: Fine Hall 314

Ergodic Theory and Statistical Mechanics Seminar
Topic: Variations on Szemeredi's Theorem
Presenter: Bryna Kra, Penn State University
Date: Thursday, May 3, 2001, Time: 2:00 p.m., Location: Fine Hall 401
Abstract: Van der Waerden proved that if you color the integers in finitely many colors, then one of the colors contains arithmetic progressions of arbitrary length; Szemeredi proved the density version of this theorem.  Fustenberg gave an ergodic theoretic proof based on multiple recurrence, leading to the study of "non-conventional" ergodic averages.  In this talk, I plan to give an overview of recent results on such averages.  For example, we prove a version of Furstenberg's ergodic theorem (corresponding to arithmetic progressions of length four) with restrictions on return times.  More specifically, for a measure preserving system $(X, \CB, \mu, T)$ and a subset $E \subset X$ of positive measure, we show that there exists an odd $n$ with $\mu(E \cap T^{-n}E\cap T^{-2n} E\cap T^{-3n}E)> 0$, > so long as $T^2$ is ergodic.

Topology Seminar
Topic: Invariants of Legendrian links
Presenter: Lenny Ng, MIT
Date: Thursday, May 3, 2001, Time: 4:00 p.m., Location: Fine Hall 314

Princeton/IAS/Rutgers Number Theory Seminar
Topic: TBA
Presenter: Johan de Jong , M.I.T.
Date: Thursday, May 3, 2001, Time: 4:30 p.m., Location: Fine Hall 322

Graduate Student Seminar
Topic: Multiplier operators in tratified groups
Presenter: Ricardo Saenz, Princeton University
Date: Friday, May 4, 2001, Time: 1:00 p.m., Location: Fine Hall 214
Abstract: We will discuss the boundedness of the operator m(L), where L is a sublaplacian of the stratified group G, and m is a bounded function. By the spectral theorem, m(L) is bounded in L^2(G). However, if m satisfies a regularity condition of order Q/2, where Q is the homogeneous dimension of G, then m(L) is also bounded in L^p(G), for 1<p<\infty. We will also show that, if G is the Heisenberg group, or in general is an H-type group, then a regularity condition of order D/2 is suficient, where D is the real dimension of G (in general D < G). These results are analogous to the Hörmander-Mihilin multiplier theorem on R^n.

Geometry Seminar
Topic: Convex hypersurfaces of prescribed curvature
Presenter: Guan Bo, University of Tennessee
Date:  Friday, May 4, 2001, Time:  3:00 pm,  Location:  Fine Hall 314

Geometry Seminar
Topic:  Nonabelian gap theorem and restricted holonomy
Presenter: C. Margerin,  Ecole Polytechnique
Date:  Friday, May 4, 2001, Time:  4:00 pm,  Location:  Fine Hall 314

Week of May 7 - May 11,  2001

PACM Colloquium
Topic: Time-dependent Taylor Vortices in Wide-Gap Spherical Couette Flow
Presenter:  Rainer Hollerbach, Geosciences, Princeton University
Date: Monday, May 7, 2001, Time:  4:00 p.m., Location: Fine Hall 224

Noetherian Ring Seminar
Topic: TBA
Presenter: Karen L. Collins, Wesleyan University
Date: Wednesday, May 9, 2001, Time: 4:00 p.m., Location: Fine Hall 322

Geometry Seminar
Topic:  Equivariant de Rham torsions
Presenter: Sebastian Goette, Tuebingen
Date:  Friday, May 11, 2001, Time:  4:00 pm,  Location:  Fine Hall 314