Topic: Invariant measures for randomly forced nonlinear PDEs and the problem November 16

of turbulence

Speaker: Sergei Kuksin, Heriot-Watt/Steklov

Topic: Rational points close to an arc of a curve November 16 at IAS

Presenter: Martin Huxley, University of Wales, Cardiff

Topic: Mapping class groups and rigidity November 16

Presenter: Richard Wentworth, Johns Hopkins University

Topic: Sharp Sobolev-Poincare inequalities on compact Riemannian manifold November 17

Presenter: Emmanuel Hebey, Universite de Cergy-Pontoise

Topic: New thoughts on Sobolev spaces November 20

Presenter: Haim Brezis, Université de Paris VI and Rutgers University

Topic: The Sylvester-Gallai Theorem and Metric Spaces November 21

Presenter: Vasek Chvatal, Rutgers University

Topic: Is M_{g,n} a Mori dream space (mod p)? November 21

Presenter: Sean Keel, University of Texas

Topic: The PCT theorem and local observables November 21

Presenter: Jakob Yngvason, University of Vienna

Topic: The monodromy matrix, the adiabatic WKB method and the spectrum November 22

of quasi-periodic operators on the real line

Presenter: Frederic Klopp, University of Paris

Topic: Harmonic analysis on the infinite symmetric group November 27

Presenter: Alexei Borodin, University of Pennsylvania

Topic: Non-uniform structures in granular and gas-solid flows November 27

Presenter: Sankaran Sundaresan, Chemical Engineering, Princeton University

Topic: Nonperturbative analysis of a Model Quantum System under Time November 29

Periodic Forcing: Generic and Exceptional Cases

Presenter: Ovidiu Costin, Rutgers University

Abstract: We analyze the time evolution of a one-dimensional quantum system with an attractive delta function potential whose strength is subjected to a time periodic (zero mean) parametric variation $\eta(t)$. The amplitude of $\eta$ is unrestricted. We show that for generic $\eta(t)$, which includes the sum of any finite number of harmonics, the system, started in a localized state, gets fully ionized (the particle leaves the bound state) as time grows indefinitely, irrespective of the magnitude or frequency (resonant or not) of $\eta(t)$. There are however exceptions to full ionization which while very non-generic include rather simple explicit functions. For these $\eta(t)$ the system evolves to a nontrivial localized stationary state which is related to eigenfunctions of the Floquet operator.

Topic: TBA November 29

Presenter: H. Hofer, Courant Institute and Princeton University

Topic: TBA November 30

Presenter: V. Shokurov, Johns Hopkins University

Topic: TBA December 1

Presenter: Wang Guo-Fang, Max Planck Institute

Topic: d-bar-regularity for weakly pseudoconvex domains in compact Hermitian December 4

symmetric spaces with respect to invariant metrics

Presenter: Yum-Tong Siu, Harvard University

Topic: TBA December 4

Presenter: Salvatore Torquato, Chemistry, Princeton University

Topic: The Theta Body and Partitionable Graphs December 5

Presenter: Bruce Shepherd, Lucent Technologies

Topic: The moduli space of cubic surfaces is complex hyperbolic December 5

Presenter: Jim Carlson, University of Utah

Topic: Billiards in Rational Polygons and Moduli Spaces of Holomorphic Differentials December 6

Presenter: Alex Eskin, University of Chicago

Abstract: A polygon is called rational if all angles are rational multiples of pi. It turns out that the problem of counting periodic billiard trajectories on such a polygon can be reduced to a certain dynamical problem of the moduli space of pairs (M,w) where M is a Riemann surface, and w is a holomorphic 1-form on M. Even though it is not locally homogeneous, this moduli space is analogous in many ways to the moduli space of Euclidean lattices SL(n,R)/SL(n,Z). I will discuss these constructions and some associated problems in combinatorial enumeration.

Topic: Ricci Curvature, Minimal Volumes, and Seiberg-Witten Theory December 8

Presenter: Claude Le Brun, SUNY Stony Brook

Topic: Brownian Dynamics Methods for the Solution of Complex Polymeric December 11

Flows Based on Kinetic Theory Models: Early (CONNFFESSIT) and

More Recent (Configuration Field) Approaches

Presenter: Antony N. Beris, University of Delaware

Abstract: In the past, closed-form continuous models have been used for the solution of complex (i.e. multidimensional and/or time dependent) flow problems involving polymer solutions or melts. However, those models involve closure approximations that result in unpredictable errors in the complex flows that they are employed. Nevertheless, the presence of one or more internal variables makes the dimensionality of the microscopic problem prohibitively large to allow for a direct solution of the microscopic equations (such as those arising from kinetic theory) in even the simplest multidimensional flow problems. Fortunately, in the last decade new methodologies has emerged that allow for such solutions to be obtained at significantly less computational cost through the coupling of a stochastic solution for the polymer chain configuration to a more traditional macroscopic finite-element or spectral flow approximation of the momentum and continuity equations. In this presentation, after reviewing the first of these approaches (called CONNFFESSIT) which has first been developed by Laso and Oettinger, we will discuss the more recently developed (by Hulsen and co-workers) configuration fields approach that result in even more reduced computational requirements.

Topic: Coherent and Dissipative Electronic Transport in Aperiodic Media December 12

Presenter: Jean V. Bellissard, Universite Paul Sabatier, Toulouse, France and Institut Universitaire de France