Around symplectic cohomology

Short introductory lectures

I'll talk about an invariant of symplectic manifolds which goes by the (rather undescriptive) name of "symplectic cohomology". This invariant depends on a choice of coefficient ring, typically taken to be the integers or the integers mod 2. New technology allows one to define symplectic cohomology over the sphere spectrum. The resulting theory is expected to acquire some additional structures which I will explain.