## Weak Stability Boundary and Capture in the Three-Body Problem

GEOMETRY/DYNAMICAL SYSTEMS

Edward Belbruno

NASA/AISR & IOD, Inc.

January 19, 2011

GEOMETRY/DYNAMICAL SYSTEMS

Urs Frauenfelder

Seoul National University

January 19, 2011

GEOMETRY/DYNAMICAL SYSTEMS

The restricted 3-body problem has an intriguing dynamics. A deep observation of Jacobi is that in rotating coordinates the problem admits an integral. In joint work with P. Albers, G. Paternain and O. van Koert, we proved that the corresponding energy hypersurfaces are contact for energies below and slightly above the first critical value.

Ankur Moitra

Massachusetts Institute of Technology

January 18, 2011

Sergei Vassilvitskii

Yahoo! Research

January 17, 2011

Fred Cohen

University of Rochester; Member, School of Mathematics

January 10, 2011

Topological spaces given by either (1) complements of coordinate planes in Euclidean space or (2) spaces of non-overlapping hard-disks in a fixed disk have several features in common. The main results, in joint work with many people, give decompositions for the so-called "stable structure" of these spaces as well as consequences of these decompositions.

This talk will present definitions as well as basic properties.

David Huse

Princeton University; Member, School of Mathematics

December 17, 2010

**ANALYSIS/MATHEMATICAL PHYSICS SEMINAR**

Andrei Jorza

Institute for Advanced Study

December 16, 2010

To a regular algebraic cuspidal representation of GL(2) over a quadratic imaginary field, whose central character is conjugation invariant, Taylor et al. associated a two dimensional Galois representation which is unramified at l different from p outside a finite set of places. The first half of this talk concerns the crystallinity of the Galois representation at p , under a technical assumption. The second half of the talk is on recent work towards local-global compatibility (on GSp(4) and its implication for GL(2)).

Edward Witten

Institute for Advanced Study

December 15, 2010

Chandrashekar Khare

Institute for Advanced Study

December 15, 2010

Iwasawa developed his theory for class groups in towers of cyclotomic fields partly in analogy with Weil's theory of curves over finite fields. In this talk, we present another such conjectural analogy. It seems intertwined with Leopoldt's conjecture. This talk is related to J-P.Wintenberger's talk here earlier this year.

Larry Guth

University of Toronto; Member, School of Mathematics

December 14, 2010

Erdos conjectured that N points in the plane determine at least c N (log N)^{-1/2} different distances. Building on work of Elekes-Sharir, Nets Katz and I showed that the number of distances is at least c N (log N)^{-1} . (Previous estimates had lower bounds like N^{.86}.)