Symplectic Geometry (2010, Mastermath, UU)

Course Description

Symplectic geometry is the study of manifolds equipped with a closed nondegenerate two form. It is the modern language for classical mechanics, notably in the Hamilton formalism.
The following subjects will be discussed in the lectures:

• Symplectic linear algebra
• Symplectic manifolds
• Hamilton formalism
• Integrable systems
• Moment map geometry

Prerequisites

This is a basic course for students in the first year of the master. We only assume some familiarity with the concept of manifold.

Examination

Written exam: January 19, 2011. 13:30-16:30h in the Educatorium Betazaal. The exam is not open book. However you are allowed to make a summary of at most one page, which you can use to remember the various formulas. I will check these at the beginning of the exam. More than one page is not allowed!

Grading

Literature

Lecture notes can be found here. These notes will be updated weekly.

Locations, material covered and exercises

• Week 37, BBL 283, Ch. 1.
• Week 38, BBL 283, Ch. 2, 2.1 and 2.2.
• Week 39, Unnikgebouw room 220, Ch. 2, 2.3 till 2.6, exercise 2.4 and proof Cartan formula.
• Week 40, Unnikgebouw zaal Groen, Ch. 2, 2.7, Ch. 3, 3.1 and 3.2, exercise 2.10.
• Week 41, Unnikgebouw zaal Groen, Ch. 3, 3.3 and 3.4, exercise 3.2.
• Week 42, Unnikgebouw zaal Groen, Ch 3.5 and 3.6, no homework exercise
• Week 43, Unnikgebouw room 220, Ch 3.7 and 4.1, exercise 3.8
• Week 44, Unnikgebouw zaal Groen, Ch 4.2 and half of 4.3, exercise 4.1
• Week 45, Minnaert Building room 208, Ch 4.3 and 4.4, exercises 4.5 & 4.9 & 4.10
• Week 46, BBL 023, Ch 5.1, exercises 5.1 and 5.2
• Week 47, Unnikgebouw zaal Groen, Ch 5.2 upto Corollary 5.11, Homework: Understand Ch 5.2
• Week 48, Unnikgebouw zaal Groen, Ch 5.3, Homework: exercises 3.5 and 3.6
• Week 49, Unnikgebouw zaal Groen, Ch 5.4, Homework: exercises 5.9 and 5.10