Topic: Dynamics of the Discretized Swift-Hohenberg Equation February 4

Presenter: Yakov Pesin, Pennsylvania State University

Topic: On the Lego--Teichmuller game February 4

Presenter: A. Kirillov, Jr., IAS

Abstract: For a smooth oriented surface S, denote by M(S) the set of all ways to represent S as a result of gluing

together standard spheres with holes (``the Lego game''). In this paper we give a full set of simple moves and

relations which turn M(S) into a connected and simply-connected 2-complex. This gives the generators and relations for

the tower of mapping class groups (Teichmuller groupoid).

Results of this kind were first obtained by Moore and Seiberg, but their paper contained serious gaps. Our proof is

based on a different approach, which allows us to get a rigorous proof.

Presenter: H. Iwaniec, Rutgers University

Topic: Symplectic forms in the theory of solitons February 5

Presenter: Duong Hong Phong, Columbia University

Topic: Birkhoff families, geodesic excursions and Khinchin's Theorem February 8

Presenter: Dmitry Kleinbock, Rutgers University

Topic: Brushlets: a tool for directional image analysis and image compression February 9

Presenter: Francois Meyer, Yale University

Topic: An algebra of integral operators and correlation February 10

functions of interacting electron gas

Presenter: Vladimir Korepin, SUNY, Stony Brook

Topic: Asymptotic Aspects in Geometric Functional Analysis February 10

Presenter: Nicole Tomczak-Jaegermann, University of Alberta

Abstract: We shall present several directions in which close connections can be found between the geometry and

linear-metric structure of infinite-dimensional Banach spaces and finite-dimensional phenomena. The geometry of convex

bodies in $R^n$ has a fundamental influence on structural phenomena in random quotients of the corresponding normed

spaces; and this in turn can be used in infinite-dimensional constructions with various non-local properties.

Topic: Pointwise Theorems for Amenable Groups February 11

Presenter: Elon Lindenstrauss, Hebrew University

Abstract: The classical ergodic theory deals with measure preserving Z actions. Since the 50's, it has become

increasingly clear that most of the results of the classical ergodic theory can be extended to actions of amenable groups,

i.e. groups for which there exists an invariant mean.

Somewhat surprisingly, two of the basic theorems of ergodic theory, the pointwise ergodic theorem and the

Shannon-McMillan Breiman theorem were not known for general amenable groups. I will describe a proof of these two

theorems for actions of discrete groups (these techniques should work also in more general contexts).

Topic: Down-up algebras February 11

Presenter: G. Benkart, University of Wisconsin, Madison

Abstract: Down-up algebras originated in the study of differential posets. These algebras exhibit many remarkable

features and many interesting connections with enveloping algebras of Lie algebras, Weyl algebras, quantum groups, and

Witten's deformations of the enveloping algebra of sl(2). This talk will focus on their combinatorial origins,

representations, and structure.

Topic: Functional on Kahler manifolds February 12

Presenter: E. Calabi, University of Pennsylvania

Topic: Wave maps in 2+1 dimensions February 15

Presenter: Daniel Tataru, Northwestern University

Topic: Nonlinear hyperbolic equations February 17

Presenter: Daniel Tataru, Northwestern University

Abstract: We present some recent results concerning the local theory for nonlinear second order hyperbolic equations

with nonsmooth initial data. These results are based on some ne strichartz type estimates for hyperbolic operators with

nonsmooth coefficients.

Topic: Applications of Homogeneous Dynamics to Diophantine February 18 & 25

Approximation on Manifolds

Presenter: Dmitry Kleinbock, Rutgers University

Topic: Applications of Homogeneous Dynamics to Diophantine February 18 & 25

Approximation on Manifolds

Presenter: Dmitry Kleinbock, Rutgers University

Topic: The Nash Conjective for Threefolds February 25

Presenter: Janos Kollar, University of Utah

Topic: Lanford's Program March 4

Presenter: Michael Yampolsky, Yale University

Topic: Statistical properties of weak Gibbs measures for certain March 25

nonhyperbolic systems

Presenter: Michiko Yuri, Sapporo University

Abstract (see attached)