Topic: Nonperturbative analysis of a Model Quantum System under Time December 6

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: 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: Induction theorems in algebra and topology II December 7

Presenter: Jesper Grodal, Institute for Advanced Study

Abstract: This will be the second talk. I will talk about how homology decompositions and homotopy colimits of classifying spaces are tied to induction theorems in algebra and can be used to calculate group cohomology.

Topic: Gluing procedures for minimal and constant mean curvature surfaces: December 7

methods and applications

Presenter: Frank Pacard, University of Paris, 12

Topic: Billiards and torus covers December 7

Presenter: Alex Eskin, University of Chicago

Topic: Convergence of embedded minimal surfaces in 3-manifolds and removable December 7

singularities for minimal laminations

Presenter: Bill Minicozzi, Johns Hopkins University

Topic: Structures of Quantum Field Theory December 8

Presenter: Slava Rychkov

Abstract: In 2 lectures (12/1/00 and 12/8/00) I will try to give an exposition of basic objects and ideas of Quantum Field Theory. The list of topics will include: Feynman path integrals, Wightman axiomatics, Feynman diagram techniques for perturbation theory, renormalization group, and conformal field theories. If time permits, we will discuss asymptotic freedom and mass gap in gauge field theories, which is the subject of one of the $1,000,000 Clay Institute Problems. No prior knowledge of QFT will be assumed.

Topic: Real structures on complex surfaces: existence, finiteness, and quasi-simplicity December 8 (please note different

Presenter: V. Kharlamov, University of Strasbourg time and day)

Abstract: The subject of the talk is motivated by recent achievements in topological and deformation theories of real algebraic surfaces. It will concern some particular, previously almost ignored, questions like the possibility to deform a complex surface into a surface with a real structure, finiteness of real structures, or the relation between deformation and topological equivalences of real structures. I will survey the few results obtained in this direction.

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

Presenter: Claude Le Brun, SUNY Stony Brook

Topic: Mixed norm estimates for a model restricted X-ray transform December 11

Presenter: Burak Ergodan, Caltech

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

Topic: TBA December 13

Presenter: Giovanni Gallavotti, Rome University and Rutgers University

Topic: TBA December 14

Presenter: Fabrice Bethuel, University of Paris VI