Topic: Segregation in the Falicov-Kimball model April 18

Presenter: Daniel Ueltschi, Princeton University

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.

Topic: Amenable groups and their actions April 18

Presenter: Benjamin Weiss, Hebrew University of Jerusalem

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.

Topic: Gibbsian Dynamics and Ergodicity for some Stochastically Forced Dissipative April 19

Equations

Presenter: Di Liu, Princeton University

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.

Topic: On the distribution of geodesics according to their rotation numbers (on a April 19

negatively curved manifold)

Presenter: Nalini Anantharaman

Topic: Is the geometric genus of a surface singularity topological ? April 19

Presenter: Andras Nemethi, Ohio State University

Topic: Finding Arithmetic Progressions April 19 IAS

Presenter: Ben Green, Princeton University and Cambridge University

Topic: The wonderful world of CR geometry April 20

Presenter: Andreea Nicoara, Princeton University

Abstract: This will be a very introductory lecture on CR (Cauchy-Riemann) geometry. I will define CR manifolds and discuss the kinds of problems that arise in this field along with some of the methods used to attack them. I might even touch upon Penrose's application of CR geometry to relativity which is the only non-mathematical application, as far as I know.

Topic: Complex vector bundles and applications to linear partial differential equations April 20

Presenter: Howard Jacobowitz

Topic: On KdV and completely integrable systems April 23

Presenter: François Trèves, Rutgers University

Topic: Unavoidable and Avoidable Crossings in the Plane April 24

Presenter: János Pach, New York University

Topic: Concordant sequences and integer-valued entire functions April 24

Presenter: Jonathan Pila, Melbourne, Australia

Topic: Hyperbolicity,diophantine approximation and complex two ball quotients April 24

Presenter: S.K.Yueng, Purdue University

Topic: Quantum Pumps April 25

Presenter: Yosi Avron, Technion, Haifa

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.

Topic: An ergodicity problem in the theory of Brownian Motion April 26

Presenter: Meir Smorodinsky, Telaviv University

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.

Topic: Gluing formulae for Seiberg-Witten invariant along 3-dimensional torus April 26

Presenter: B. Doug Park, McMaster University

Abstract: In 1994, Seiberg and Witten introduced a very useful diffeomorphism invariant of smooth 4-manifolds. In 1997, Morgan, Mrowka and Szabo gave fundamental gluing formulae for computing the SW-invariants of a closed 4-manifold that is gotten by gluing together D^2 x T^2 (disk cross 2-torus) and an arbitrary 4-manifold whose boundary is also T^3. In this talk, we will present a new gluing formula for the SW-invariant along T^3, which should work in more general situations. In particular, the new formula does not require that one of the glued-up halves is D^2 x T^2. We will try to make the talk accessible to the non-experts.

Topic: Stark's Question and a Strong Form of Brumer's Conjecture April 26

Presenter: Cristian Popescu, Johns Hopkins

Topic: Negative sectional curvature metrics on 3-manifolds with boundary April 27

Presenter: Joel Hass, Institute for Advanced Study and University of California at Davis

Topic: TBA April 30

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

Topic: TBA May 1

Presenter: Jeff Kahn, Rutgers University

Topic: TBA May 3

Presenter: Lenny Ng, MIT

Topic: TBA May 3

Presenter: Johan de Jong, M.I.T.

Topic: TBA May 4

Presenter: Guan Bo, University of Tennessee

Topic: TBA May 4

Presenter: C. Margerin, Ecole Polytechnique

Topic: Time-dependent Taylor Vortices in Wide-Gap Spherical Couette Flow May 7

Presenter: Rainer Hollerbach, Geosciences, Princeton University

Topic: Equivariant de Rham torsions May 11

Presenter: Sebastian Goette, Tuebingen