Clay Mathematics Institute

Dedicated to increasing and disseminating mathematical knowledge

Evolution Equations

June 23 - July 18, 2008

Eidgenössische Technische Hochschule, Zürich, Switzerland

Organizers: David Ellwood, Igor Rodnianski, Gigliola Staffilani, Jared Wunsch

Designed for graduate students and postdocs, the program will focus on recent progress in the theory of evolution equations.  Such equations lie at the heart of many areas of mathematical physics, arising not only in situations with a manifest time evolution (such as liner and nonlinear wave and Schrödinger equations) but also in the high energy or semi-classical limits of elliptic problems.  Mathematical problems as diverse as stability and singularity formation in relativity, mathematical theory of black holes, existence and blow-up of solutions to nonlinear Schrödinger equations, semi-classical asymptotics of quantum-mechanical energy states, and quantum many body scattering theory all turn out to be susceptible to analysis by a remarkably unified set of techniques.  

The first three weeks of the school will consist of three parallel courses introducing these techniques together with some applications. The fourth week will consist of mini-courses focusing on more advanced topics.

Foundational Courses

Microlocal Analysis, Spectral and Scattering Theory
Jared Wunsch, Rafe Mazzeo

The Theory of the Nonlinear Schrödinger Equation
Gigliola Staffilani, Pierre Raphaël

Wave Equation and Evolution  Problems in General Relativity
Igor Rodnianski, Mihalis Defermos


Derivation of Effective Evolution Equations from Microscopic Quantum Dynamics
Benjamin Schlein

Nonlinear Schrödinger Equations at Critical Regularity
Monica Visan

Wave Maps with and without Symmetries
Michael Struwe

Quantum N-body Scattering, Diffraction of Waves, and Symmetric Spaces
András Vasy