Johns Hopkins University
 Department of Mathematics
 404 Krieger Hall
 3400 N. Charles Street
 Baltimore, MD 21218

 410-516-7397 Phone
 410-516-5549 Fax

Abstracts for Kempf Lecturer Series

Wilhelm Schlag

On the Schroedinger flow on surfaces of revolution

I  will discuss  recent  work on  the  decay for the Schrödinger flow on surfaces of revolution (joint with Avy Soffer, Rutgers, and Wolfgang Staubach, U of Chicago).  Such surfaces are basic exampled of non-compact manifolds with trapped geodesics.
 

Tuesday, Sept 5, 4-5pm
Homewood Campus
Building: Krieger   Room: 308

 

  Wilhelm Schlag

 Dispersive estimates for wave equations and applications to stability of solitons (II)

We will discuss recent work on the conditional stability of otherwise unstable nonlinear bound states (solitary waves) of certain semi-linear wave equations. This will rely partially on a very detailed understanding of the long-time behavior of the linearized flow around such solitary waves. The symmetries of the nonlinear equation lead to singularities of the spectral measure of the linearized flow which can be either eigenvalues or resonances. These destroy the dispersive behavior of the linearized flow but only on a finite-dimensional subspace.  We will describe the relevance of this subspace with regard to what is commonly known as "modulation theory".

The nonlinear work is largely joint with Joachim Krieger (Harvard), whereas the linear work is partially joint with Michael Goldberg (JHU) and Burak Erdogan (UIUC).

Friday, Sept 8, 4-5 pm
Homewood Campus
Building: Krieger   Room: 308