Topic: Some singular quantum mechanical examples February 1

Presenter: John Stalker, Princeton University

Abstract: Most of perturbation theory is based on the assumption that, if a Hamiltonian depends in some reasonable way

on a parameter, the probability of a transition from one state to another should also depend nicely on this parameter. I

will present two simple examples to show that this assumption is often very far from correct. The first example is the

harmonic oscillator and the second is a variant of the classical "particle in a box" problem.

Topic: A study of Behaviour of the Stresses in Reinforced February 1

Composites with Closely Spaced Fibers

Presenter: Michael Vogelius, Rutgers University

Topic: On the structure of classical Iwasawa modules February 2

Presenter: Kazuhiro Fujiwara, IAS

Topic: "Statistical mechanics of anharmonic chains coupled to two heat baths" February 3

Presenter: Luc Rey-Bellet, Rutgers University

Topic: Information Theory and Fractal Geometry February 3

Presenter: Hillel Furstenberg, Hebrew University

Abstract: The intersection theory of fractals in Euclidean space is quite different from that of algebraic and differentiable

varieties. Thus one can construct two fractal sets, A and B in R^m each of (full) dimension m, such that every translate of

A meets B in at most one point. However for "good" pairs of fractals the traditional inequality holds: for some translate

A', the codimension of the intersection of A' and B is less than or equal to the sum of the codimensions of A and B. The

proof will use information theory and the ergodic theorem.

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.

Topic: New estimates of L-functions

Presenter: H. Iwaniec, Rutgers University

Topic: Symplectic forms in the theory of solitons February 5

Presenter: Duong Hong Phong, Columbia 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 new Strichartz type estimates for hyperbolic operators with

nonsmooth coefficients.

Topic: An algebra of integral operators and correlation February 10

functions of interacting electron gas

Presenter: Vladimir Korepin, SUNY, Stony Brook

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

nonhyperbolic systems

Presenter: Michiko Yuri, Sapporo University

Abstract: See Attached