As of April 17 - 20,  2001

Discrete Mathematics Seminar  *****CANCELLED******
Topic: Symmetry and Color-Symmetry
Presenter: John Conway, Princeton University
Date: Tuesday, April 17, 2001, Time: 2:15 p.m., Location: Fine Hall 224

Topology Seminar  ***Note Special Time and Date
Topic: Change of Variable Formula for Complex Genera and Its Applications to Higher Dimensional Flops
Presenter: Chin-Lung Wang, Harvard University
Date: Tuesday, April 17, 2001, Time: 2:30 p.m., Location: Fine Hall 214

Algebraic Geometry Seminar
Topic: Syzygies over the exterior algebra and Chow forms
Presenter: F. Schreyer, University of Bayreuth
Date: Tuesday, April 17, 2001, Time: 4:30 p.m., Location: Fine Hall 322

Statistical Mechanics Seminar
Topic: Segregation in the Falicov-Kimball model
Presenter:  Daniel Ueltschi, Princeton University
Date:  Wednesday, April 18, 2001, Time:  2:00 p.m., Location:  Jadwin 343
Abstract: The Falicov-Kimball model is a simple quantum lattice model that describes light and heavy electrons interacting with on-site repulsion.  It can be seen as a simplification of the Hubbard model. By neglecting the kinetic (hopping) energy of particles of spin up, one gets Falicov-Kimball.  We show that away from half-filling, i.e. if the densities of both kinds of particles are chosen not to add to 1, the particles segregate for large enough repulsion. In the language of the Hubbard model, this means creating two regions with positive and negative magnetization.  The key is a lower bound for the sum of eigenvalues of the discrete Laplace operator (hopping matrix) in an arbitrary domain, with Dirichlet boundary conditions. The lower bound consists of a bulk term, independent of the shape of the domain, and of a term proportional to the boundary. Therefore, one lowers the kinetic energy of the itinerant particles by choosing a domain with small boundary. For Falicov- Kimball, this corresponds to having a unique and ``compact'' domain that is empty of heavy particles.

Departmental Colloquium
Topic: Amenable groups and their actions
Presenter: Benjamin Weiss, Hebrew University of Jerusalem
Date:  Wednesday, April 18, 2001, Time: 4:00 p.m., Location: Fine Hall 314
Abstract: After explaining what amenable groups are and why they are the natural setting for ergodic theory I will survey some new developments related to entropy, uniform mixing, and limit theorems.

Ergodic Theory and Statistical Mechanics Seminar
Topic: Gibbsian Dynamics and Ergodicity for some Stochastically Forced Dissipative Equations
Presenter:  Di Liu, Princeton University
Date: Thursday, April 19, 2001, Time: 2:00 p.m., Location: Fine Hall 401
Abstract:  We study the stationary measures for the stochastically perturbed one dimensional Ginzburg-Landau equation, Cahn-Hilliard equation and Kuramoto-Sivashingski equation with periodic boundary conditions. We proved the uniqueness of the stationary measures of these equations under the condition that all ``determining modes'' are forced. The main idea behind the proof is to study the Gibbsian dynamics of the low modes obtained by representing the high modes as functionals of the time-history of the low modes.

Ergodic Theory and Statistical Mechanics Seminar
Topic: On the distribution of geodesics according to their rotation numbers (on a negatively curved manifold)
Presenter:  Nalini Anantharaman
Date: Thursday, April 19, 2001, Time: 3:00 p.m., Location: Fine Hall 401

Topology Seminar
Topic: Is the geometric genus of a surface singularity topological ?
Presenter: Andras Nemethi, Ohio State University
Date: Thursday, April 19, 2001, Time: 4:00 p.m., Location: Fine Hall 314

Princeton University/IAS/Rutgers Number Theory Seminar
Topic: Finding Arithmetic Progressions
Presenter: Ben Green, Princeton University and Cambridge University
Date: Thursday, April 19, 2001, Time: 4:15 p.m.. Location: SH 101 at IAS

Geometry Seminar
Topic: Complex vector bundles and applications to linear partial differential equations
Presenter:  Howard Jacobowitz
Date:  Friday, April 20, 2001, Time:  4:00 pm, Location:  Fine Hall 314

Week of April 23 - 27,  2001

Analysis Seminar
Topic: On KdV and completely integrable systems
Presenter: François Trèves, Rutgers University
Date: Monday, April 23, 2001, Time: 4:00 p.m., Location: Fine Hall 314

Discrete Mathematics Seminar
Topic: Unavoidable and Avoidable Crossings in the Plane
Presenter: János Pach, New York University
Date: Tuesday, April 24, 2001, Time: 2:15 p.m., Location: Fine Hall 224

Princeton/IAS Number Theory Seminar  ***Note special day, time, and location
Topic: Concordant sequences and integer-valued entire functions
Presenter: Jonathan Pila, Melbourne, Australia
Date: Tuesday, April 24, 2001, Time: 3:30 p.m., Location: Fine Hall 314

Algebraic Geometry Seminar
Topic: Hyperbolicity,diophantine approximation and complex two ball quotients
Presenter: S.K.Yueng, Purdue University
Date: Tuesday, April 24, 2001, Time: 4:30 p.m., Location: Fine Hall 322

Statistical Mechanics Seminar
Topic: Quantum Pumps
Presenter:  Yosi Avron, Technion, Haifa
Date:  Wednesday, April 25, 2001, Time:  2:00 p.m., Location:  Jadwin 343
Abstract: Quantum pumps transfer charge, energy  etc. beween electron baths. A useful description is in terms of  adiabatic scattering theory. I shall discuss notions of optimal pumps and give their geometric characterization.  This is joint work with A. Elgart, G.M. Garf and L. Sadun.

Ergodic Theory and Statistical Mechanics Seminar
Topic: An ergodicity problem in the theory of Brownian Motion
Presenter: Meir Smorodinsky, Telaviv University
Date: Thursday, April 26, 2001, Time: 2:00 p.m., Location: Fine Hall 401
Abstract:  From the absolute value of a martingale, $X$, there is a unique increasing process that can be subtracted so as to obtain a martingale, $Y$. Paul Levy discovered that if $X$ is Brownian motion, $B$, then $Y$, too, is a Brownian motion.  Equivalently, Levy found that the transformation that maps $B$ to $Y$ is measure-preserving. Whether it is ergodic,was a question raised by Revuz and Yor in the book "continuous martingales and Brownian Motion". In a joint paper with Lester Dubins, it was proved that if the natural analogue of Levy's transformation for the symmetric random walk is modified to be measure-preserving, it is isomorphic to the one-sided, Bernoulli shift transformation associated with a sequence of independent random variables, each uniformly distributed on the unit interval.  In my talk I shall discuss the original question of Yor and its connecion with the symmetric random walk solution.

Topology Seminar
Topic:  SW-gluing formula along T^3
Presenter: B. Doug Park, McMaster University
Date: Thursday, April 26, 2001, Time: 4:00 p.m., Location: Fine Hall 314

Princeton/IAS/Rutgers Number Theory Seminar
Topic: Stark's Question and a Strong Form of Brumer's Conjecture
Presenter: Cristian Popescu, Johns Hopkins University
Date: Thursday, April 26, 2001, Time: 4:30 p.m.. Location: Fine Hall 322

Geometry Seminar
Topic: Negative sectional curvature metrics on 3-manifolds with boundary
Presenter: Joel Hass,  Institue for Advanced Study and University of California at Davis
Date:  Friday, April 27, 2001, Time:  4:00 pm,  Location:  Fine Hall 314

Week of April 30 - May 4,  2001

PACM Colloquium
Topic:  TBA
Presenter:  Eric Vanden-Eijnden, CIMS, New York University
Date: Monday, April 30, 2001, Time:  4:00 p.m., Location: Fine Hall 224

Discrete Mathematics Seminar
Topic: TBA
Presenter: Jeff Kahn, Rutgers University
Date: Tuesday, May 1, 2001, Time: 2:15 p.m., Location: Fine Hall 224

Topology Seminar
Topic: TBA
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

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

Geometry Seminar
Topic: TBA
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

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