Instructor: Jan Segert

Description: The course will cover the foundations of Riemannian geometry and symplectic geometry on manifolds. The exposition will emphasize the relationship between modern coordinate-free techniques and classical coordinate-based techniques, and choosing an appropriate balance between the two techniques for proving theorems and for concrete computations. We will also cover the basics of Lie groups and their roles as symmetry groups.

We will apply these techniques to study the local and global behavior of spinning tops and related classical problems in mechanics. We will also use the classical mechanics problems to explore some basic features of integrable systems.

Prerequisite: 8250 [403] or equivalent.