Title: Smoothing effects for the Schr\"odinger evolution October 4

Presenter: Igor Rodnianski, Princeton University

Abstract: We study the spatial regularity of the solutions of the linear time-dependent Schr\"odinger equation. The first case considered is the motion of a quantum particle in the electric field of a subquadratic potential. We describe the connection between the decay of the initial data at infinity and the consequtive improvement of regularity. We then consider the periodic Schr\"odinger equation and establish that the "smoothness" of the propagator at time $\,t\,$ depends upon the diophantine properties of $\,t$. The formation of "quantum fractals" is also discussed.

Title: Dynamics of Pattern Formation in a Binary Epilayer October 4

Presenter: Zhigang Suo, Princeton University

Title: Numerical Determination of Chaotic Transfers; or, Orbit Design October 5

for Cheap Spaceflight

Presenter: Edward Belbruno, PACM & IOD

Abstract: Over the past decade, a simple method has been developed which numerically estimates regions in the Newtonian three and four-body problems, and in the solar system, which give rise to an interesting unstable chaotic motion with applications to spaceflight and astronomy. The boundaries of these regions are not well defined, and are 'fuzzy'. Orbits passing through these regions, called 'weak stability boundaries' (WSB's) have interesting properties for applications to the motions of spacecraft and natural objects such as asteroids. They can be used to construct very low energy, ie cheap, transfers to the moon and other destinations, which are different from standard routes. One of these routes for going to the moon was operationally demonstrated in 1991. NASA is planning to incorporate WSB transfers for a new mission to Europa of Jupiter, and to Mars. Resonance properties of WSB transfers have interesting applications to the motions of Kuiper belt objects outside the orbit of Neptune, and for short period comets passing

near Jupiter. Up to very recently, the WSB approach has been slowly catching on, and now it is gaining more acceptance. The purpose of this seminar is to describe how to numerically determine WSB transfers. That is, what are the actual details of doing this. There will be fun computer simulations, and interesting applications. WSB Theory represents the first systematic application of unstable chaos to spacecraft motion for transfers. The end result is that spaceflight can be made cheap in a number of cases.

Title: Equidistribution of Hecke orbits on GL(n) and GSp(2g) October 5

Presenter: Emmanuel Ullmo, Princeton University

Title: Adiabatic limit for charged particles and their radiation fields October 6

Presenter: Herbert Spohn, Technical University Munich

Title: Integrable Geodesicd I-laws with positive topological entropy October 7

Presenter: I. Taimanov, Rutgers University

Title: Introduction to Symplectic Field Theory I October 7

Presenter: Y. Eliashberg, Princeton University & Stanford University

Title: Bounded cohomology of lattices in semisimple groups October 8

Presenter: Marc Burger, ETH

Title: Critical metrics for special values of spectral zeta functions October 11

Presenter: Kate Okikiolou, UC San Diego & Princeton University

Title: Extremals for sharp Sobolev inequalitie October 13

Presenter: Emmanuel Hebey, University Cergy-Pontoise

Title: A New Rigidity of Furstenberg Entropy October 14

Presenter: Amos Nevo, Princeton University

Title: Introduction to Symplectic Field Theory II October 14

Presenter: Y. Eliashberg, Princeton University & Stanford University

Title: Numerical Determination of Chaotic Transfers; or, Orbit October 15

Design for Cheap Spaceflight

Presenter: Edward Belbruno, PACM & IOD

Title: Mathematical diffraction theory October 15 (special day)

Presenter: Michael Baake, University of Tuebingen

Title: To Be Announced October 15

Presenter: Steve Altschuler and Lani Wu, Microsoft

Title: Gromov's a-T-menable groups: non-rigidity in representation theory October 18

Presenter: Alain VALETTE (Neuchatel, Switzerland)

Abstract: A locally compact group is a-T-menable, or satisfies the Haagerup property, if it admits a continuous, isometric, proper action on some affine Hilbert space. We shall give other equivalent definitions (in representation theory and in ergodic theory), all showing that a-T-menability is a strong negation of Kazhdan's property (T). After discussing the interest of this class of groups, we shall prove that the following groups are a-T-menable: amenable groups, SO(n,1) and SU(m,1), groups acting properly on trees. Finally, we classify connected Lie groups which are a-T-menable.

Title: Structure of clusters near percolation threshold October 20

for 2D continuum percolation

Presenter: Madeleine Sirugue, University of Marseille

Title: TBA October 21

Presenter: Jack Morava, John Hopkins University

Title: Numerical Determination of Chaotic Transfers; or, Orbit Design October 22

for Cheap Spaceflight

Presenter: Edward Belbruno, PACM & IOD

No seminars scheduled at this time

Title: Numerical Determination of Chaotic Transfers; or, Orbit Design November 2

for Cheap Spaceflight

Presenter: Edward Belbruno, PACM & IOD