Buch, Englisch, Band 7, 430 Seiten, Gewicht: 765 g
Buch, Englisch, Band 7, 430 Seiten, Gewicht: 765 g
Reihe: IAS/Park City Mathematics Series
ISBN: 978-0-8218-4095-5
Verlag: American Mathematical Society
Symplectic geometry has its origins as a geometric language for classical mechanics. But it has recently exploded into an independent field interconnected with many other areas of mathematics and physics. The goal of the IAS/Park City Mathematics Institute Graduate Summer School on Symplectic Geometry and Topology was to give an intensive introduction to these exciting areas of current research. Included in this proceedings are lecture notes from the following courses: Introduction to Symplectic Topology by D. McDuff; Holomorphic Curves and Dynamics in Dimension Three by H. Hofer; An Introduction to the Seiberg-Witten Equations on Symplectic Manifolds by C. Taubes; Lectures on Floer Homology by D. Salamon; A Tutorial on Quantum Cohomology by A. Givental; Euler Characteristics and Lagrangian Intersections by R. MacPherson; Hamiltonian Group Actions and Symplectic Reduction by L. Jeffrey; and Mechanics: Symmetry and Dynamics by J. Marsden. Information for our distributors: Titles in this series are copublished with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
- Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung
- Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
- Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
- Mathematik | Informatik Mathematik Topologie Algebraische Topologie
- Naturwissenschaften Physik Physik Allgemein
- Naturwissenschaften Physik Quantenphysik Teilchenphysik
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
- Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik
Weitere Infos & Material
Introduction
Introduction to symplectic topology
Introduction
Basics
Moser's argument
The linear theory
The nonsqueezing theorem and capacities
Sketch proof of the nonsqueezing theorem
Bibliography
Holomorphic curves and dynamics in dimension three
Problems, basic concepts and overview
Analytical tools
The Weinstein conjecture in the overtwisted case
The Weinstein conjecture in the tight case
Some outlook
Bibliography
An introduction to the Seiberg-Witten equations on symplectic manifolds
Introduction
Background from differential geometry
Spin and the Seiberg-Witten equations
The Seiberg-Witten invariants
The symplectic case, part I
The symplectic case, part II
Bibliography
Lectures on Floer homology
Introduction
Symplectic fixed points and Morse theory
Fredholm theory
Floer homology
Gromov compactness and stable maps
Multi-valued perturbations
Bibliography
A tutorial on quantum cohomology
Introduction
Moduli spaces of stable maps
$QH^*(G/B)$ and quantum Toda lattices
Singularity theory
Toda lattices and the mirror conjecture
Bibliography
Euler characteristics and Lagrangian intersections
Introduction
Lecture 1
Lecture 2
Lecture 3
Lecture 4
Lecture 5
Bibliography
Hamiltonian group actions and symplectic reduction
Introduction to Hamiltonian group actions
The geometry of the moment map
Equivariant cohomology and the Cartan model
The Duistermaat-Heckman theorem and applications to the cohomology of symplectic quotients
Moduli spaces of vector bundles over Riemann surfaces
Exercises
Bibliography
Park City lectures on mechanics, dynamics, and symmetry
Introduction
Reduction for mechanical systems with symmetry
Stability, underwater vehicle dynamics and phases
Systems with rolling constraints and locomotion
Optimal control and stabilization of balance systems
Variational integrators
Bibliography
