Spring 2005 : MAT 595 Introduction to Symplectic Geometry

Tuesday 3:00-4:40 in Altgeld 343, and Wednesday 12-12:50 in Altgeld 347.


Overview of the course

Symplectic geometry has its roots in the study of classical mechanics and now plays a major role in many areas of modern mathematics from
algebraic geometry to low dimensional topology. The primary goal of this course will be to thoroughly cover the basic concepts, examples and theorems
of symplectic geometry. We will discuss (among other things); symplectic linear algebra, symplectic manifolds, the Darboux theorem(s), Hamiltonian
dynamics, Hamiltonian group actions, moment maps and reduction. I also hope to survey some more advanced topics such as; symplectic capacities, Hofer's
geometry, and Gromov's theory of pseudo-holomorphic curves.

Course grades will be based on participation (50%) and on 4-5 Homework assignments (50%).

Homework Assignment 1, due Wed Sept 28.


Prerequisites

Basic differential geometry and topology.


Office Hours

Tuesdays and Thursdays 10:00 to 11:00, or by appointment.


References

Our primary reference will be Ana Cannas da Silva's book Lectures on Symplectic Geometry.
Some other lecture notes availible online are those by Kai Cieliebak (Part A Part B), Robert Bryant and Eckhard Meinrenken.


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This page last modified by Ely Kerman
Friday, 20-Jan-2005 13:12:53 EST
Email corrections and comments to ekerman@math.uiuc.edu