Symplectic Cohomology Construction Via C*-actions

In a series of papers with Alexander Ritter, we construct a symplectic cohomology for open non-convex symplectic manifolds that admit pseudo-holomorphic C*-actions. Out of this construction, we get a filtration on ordinary cohomology of these manifolds, which in practice is explicitly computable, using Morse-Bott-Floer spectral sequences. I will show concrete examples of ADE resolutions and low-dimensional Higgs bundles. If time permits, I will comment on the comparison with other known filtrations for the latter spaces.