Mathematics 268: Topics in Differential Geometry (Symplectic Geometry)

Mathematics 268: Topics in Differential Geometry (Symplectic Geometry) (Spring 2003)

Instructor

Description

I will be covering the fundamentals of symplectic topology and geometry.

The first third of the course will be devoted to 'classical' symplectic geometry: Lagrangians, Legendre transformations, Hamiltonians, symplectic manifolds and the Darboux-Weinstein theorem, symmetries and conservation laws and the Arnold-Liouville theorem, momentum mappings, reduction, and convexity.

The second third of the course will be devoted to developing elliptic methods: pseudo-holomorphic curves, Gromov compactness and moduli, applications to packing and (non)-squeezing theorems, etc.

The final third will cover related topics and recent developments, perhaps relations with toric varieties, representation theory, or other topics that depend on the interests of the class.

Prerequisites

Mathematics 267 (Differential Geometry) and Math 262 (Algebraic Topology II). Specifically I will assume that the students are familiar with standard topics in Riemannian geometry: manifolds, metrics, connections, curvature, differential forms, de Rham cohomology, and some basic differential topology (a la, say, Bott and Tu).

Text(s)

An introduction to Lie groups and symplectic geometry, by R. Bryant
Introduction to symplectic topology, by McDuff and Salamon

Course Website

For more information see the Course Synopsis entry and (eventually) the class website http://www.math.duke.edu/~bryant/268/index.html.

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Last modified: 29 October 2002