2003 Spring MATH 268-01
Bulletin Course Description Lie groups and related topics, Hodge theory, index theory, minimal surfaces, Yang-Mills fields, exterior differential systems, harmonic maps, symplectic geometry. Instructor: Staff
(Instructor named in bulletin description above may not be current. For current instructor, see listing below.)
Title DIFFERENTIAL GEOMETRY Department MATH Course Number 2003 Spring 268 Section Number 01 Primary Instructor Bryant,Robert L Prerequisites Prerequisite: Mathematics 267 or consent of instructor. Course Homepage www2.math.duke.edu/~bryant/268/index.html
Prerequisites
This is a second course in differential geometry. 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).
Synopsis of course content
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.
Textbooks
'An introduction to Lie groups and symplectic geometry', by R. Bryant.
'Introduction to symplectic topology', by McDuff and Salamon.
Assignments
There will be regular homework assignments
Exams
No exams.
Term Papers
No term papers.
Grade to be based on
Class participation and homework
