My friend and I subscribed to a master course on Differentiable Manifolds. We are requested to do a short (~20 pages) essay on something related to the subject and (ideally) close to our research interests. My research interest is inside Mathematical Physics: The study of abstract mathematical aspects of fundamental physics (the first that came to my mind: some sort of a mathematical introduction to Supersymmetry or String Theory). My friend is more interested on PDEs and their applications. Do you think about some field and reading that can suit us both?
Just for completeness, the course is divided in:
- Introduction to Differential Topology
- Lie Groups and Lie Algebras
- Lie Groups and Lie Algebra actions
- Introduction to Symplectic and Poisson Geometry