Cohomology of contact loci
Speaker: Hong Duc Nguyen (Basque Center for Applied Mathematics)

Time: 8h, 6/11/2020

Abstract: We construct a spectral sequence converging to the cohomology with compact support of the $m$-th contact locus of a complex polynomial. The first page is explicitly described in terms of a log resolution and coincides with the first page of McLean's spectral sequence converging to the Floer cohomology of the $m$-th iterate of the monodromy, when the polynomial has an isolated singularity. Inspired by this connection we conjecture that the Floer cohomology of the $m$-th iterate of the monodromy of $f$ is isomorphic to the compactly supported cohomology of the $m$-th contact locus of $f$, and that this isomorphism comes from an isomorphism of McLean spectral sequence with ours.

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