# Evolution Equations

Share this page *Edited by *
*David Ellwood; Igor Rodnianski; Gigliola Staffilani; Jared Wunsch*

A co-publication of the AMS and Clay Mathematics Institute

This volume is a collection of notes from
lectures given at the 2008 Clay Mathematics Institute Summer School,
held in Zürich, Switzerland. The lectures were designed for
graduate students and mathematicians within five years of the Ph.D.,
and the main focus of the program was on recent progress in the theory
of evolution equations. Such equations lie at the heart of many areas
of mathematical physics and arise 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.

The three main courses focused primarily on microlocal
analysis and spectral and scattering theory, the theory of the
nonlinear Schrödinger and wave equations, and evolution problems in
general relativity. These major topics were supplemented by several
mini-courses reporting on the derivation of effective evolution equations from
microscopic quantum dynamics; on wave maps with and without
symmetries; on quantum N-body scattering, diffraction of waves, and
symmetric spaces; and on nonlinear Schrödinger equations at critical
regularity.

Although highly detailed treatments of some of these topics are now
available in the published literature, in this collection the reader
can learn the fundamental ideas and tools with a minimum of technical
machinery. Moreover, the treatment in this volume emphasizes common
themes and techniques in the field, including exact and approximate
conservation laws, energy methods, and positive commutator arguments.

Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

#### Readership

Graduate students and research mathematicians interested in partial differentital equations and mathematical physics.