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 !
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.