Math 597E: Symplectic Geometry Fall 2002

Instructor: Ben Davis
Email: bdavis@math.psu.edu
Web: http://www.math.psu.edu/bdavis/
Office: McAllister 322
Office Phone: 863-2036
Office Hours: W 1-2, F 2-3.

Text: Cannas da Silva, Lectures on Symplectic Geometry, Lecture Notes in Mathematics 1764, Springer-Verlag, 2001.
Homework: There will be periodic homework assignments.
Exams: There will be no exams.
Grades: Your grade is based on homework.
Missing or Late Work: Late homework may be accepted due to extenuating circumstances, and only at my discretion. Missing homework will receive a score of zero. The lowest homework score will be dropped from the calculation of your course grade.
Academic Integrity: All Penn State Policies regarding ethics and honorable behavior apply to this course.

Symplectic geometry is a subject with roots in mathematical physics, but whose branches now reach out to touch many other areas such as representation theory, complex geometry, and topology. In this course I will try to present a fast and elementary introduction to symplectic geometry. For your part, do your best to stay on top of things, and don't hesitate to come visit me in office hours. In my experience, students can learn more in office hours than in any other part of the course.

Homework and Announcements

Due Thur 12 Sept Read Lecture 3 and do Homeworks 1,2 and 3.

Due Thur 19 Sept Homework 4 on page 27.

Due Thur 26 Sept

Prove Cartan's Magic Formula. The neccessary steps are indicated on page 36.
Apply the local version of the Moser Theorem given on page 45 to X={p} to prove the Darboux Theorem given on page 7.

Due Thur 17 Oct

Homework 6 on page 50 of the text.
Problem 4 of Homework 7 on page 62 of the text.

Due Thur 24 Oct Homework 8 on page 72 of the text.

Due Thur 7 Nov

Homework 10 on page 82 of the text.
Homework 11 on page 89 of the text.
The exercise near the top of page 92.

Due Thur 26 Nov

Homework 13 on page 112 of the text.
Homework 14 on page 119 of the text.