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.