Looking for topics in symplectic geometry suitable for a 1 hour talk

Question

I am a master2 student and I am looking for a topic in symplectic geometry to make a 1 hour presentation with. I only had a short introduction course to symplectic geometry so subjects shouldn't be too advanced. It could be the proof of a nice theorem for instance.

The only idea I had so far was to introduce the basis of contact geometry as a complement to the course.

Thank in advance for your suggestions !

Did you also have the Weinstein Tubular Neighborhood Theorem ? Perhaps you should clarify what you already have done in the course. More advanced is, say, Floer homology. — Dietrich Burde, Jun 17 '16 at 09:27
We didn't do the weistein tubular neighbourhood theorem. I will look into that. Thank for the suggestion. — Thalanza, Jun 17 '16 at 09:45

score 1 · Answer 1 · answered Jul 04 '16 at 12:51

You can introduce contact geometry, or some Poisson geometry.

I also like to give examples of symplectic manifolds. $CP^n$, Delzant polytopes, coadjoint orbits, Kodaira-Thurston, ..., and study some properties of these examples.

You can relate everything to classical mechanics, e.g. Lagrange and Hamiltonian dynamics on tangent and cotangent bundle of a configuration space. Or look at an interesting system, e.g. various spinning tops.

Looking for topics in symplectic geometry suitable for a 1 hour talk

1 Answers1