# 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

### Mini-Courses

**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