Mathematical Physics Seminar

September Schedule

SPEAKER: Haim Brezis, Rutgers University
TIME/LOCATION: Thursday, September 20, 2007, 12:00pm, Hill 124
PLEASE NOTE DIFFERENT ROOM
TITLE: New Estimates for Linear Differential Systems with Data in L¹ and in Lⁿ
ABSTRACT: This is joint work with Jean Bourgain concerning well known and basic inequalities (Sobolev, L^p - regularity, etc) whichfail in
limiting cases. I will show how this failure can be "bypassed"under mild additional assumptions. I will present applications to the Laplacian, to the div
- curl system in 3-d, to differential forms in arbitrary dimension, and connections with geometric inequalities (such as the isoperimetric
inequality).

SPEAKER: Shmuel Fishman, Technion, Israel Institute of Technology
TIME/LOCATION: SEPTEMBER 27, 2007, 12:00PM
TITLE: Anderson Localization for the Nonlinear Schoedinger Equation (NLS): results and puzzles.
ABSTRACT: The NLS is relevant for the explorations of Bose-Einstein Condensates and for Nonlinear Classical Optics. A natural question is
whether Anderson Localization survives the effect of nonlinearities. Relevant experimental, numerical, heuristic and rigorous results will be
reviewed. Some our preliminary results (in collaboration with A Soffer and Y. Krivolapov), obtained in the framework of perturbation theory
will be presented.