Summer School 2008
Clay Mathematics Institute 2008 Summer School
Evolution Equations
June 23 - July 18
Eidgenössische Technische Hochschule, Zürich, Switzerland
Schedule: Week 1, Week 2, Week 3, Week 4
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 linear 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
- 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
syllabus and reading list - The Theory of the Nonlinear Schrödinger Equation
Gigliola Staffilani, Pierre Raphaël
syllabus and reading list - Wave Equation and Evolution Problems in General Relativity
Igor Rodnianski, Mihalis Dafermos
Mini-Courses
- Derivation of Effective Evolution Equations from Microscopic Quantum Dynamics
Benjamin Schlein
syllabus and abstract - Nonlinear Schrodinger Equations at Critical Regularity
Monica Visan
syllabus and abstract - Wave Maps with and without Symmetries
Michael Struwe
syllabus and abstract - Quantum N-body scattering, Diffraction of Waves, and Symmetric Spaces
András Vasy
syllabus and abstract
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