Math 7351:  Mathematical Methods of Classical Mechanics, Fall, 2024

Mathematical Methods of Classical Mechanics (Math 7351), Fall, 2024

Class Schedule:  MW 2:00-3:30,  509 Lake Hall

Instructor: Jonathan Weitsman, 521 Lake Hall; j.weitsman@northeastern.edu

Recommended reference books:

V.I. Arnold, Mathematical Methods of Classical Mechanics

A. Cannas da Silva, Lectures on Symplectic Geometry

Additional reading:

V.I. Arnold, Huygens and Barrow, Newton and Hooke

Course description: This is an introduction to Symplectic Geometry, the mathematics underlying both classical and quantum mechanics.

The course will emphasize the study of examples and computations which we hope will lead to a better understanding of the theory. 

Topics covered may include

• Introduction to Symplectic Geometry

• The moment map and Noether's theorem

• Marsden Weinstein reduction

• Toric Varieties

• Introduction to Morse Theory

• Equivariant cohomology and the localization theorem

• The Duistermaat Heckman Theorem

• Geometric Quantization

• Convex polytopes and the Euler Maclaurin formula

If there is time we may also include an introduction to gauge theory and/or Floer theory.