Explore the intricate connections between Floer cohomology and arc spaces in this advanced mathematics lecture delivered by Mark McLean from Stony Brook University. Delve into key concepts such as contact structures, Floer homology, and the deep contact locus. Examine the jet space conjecture and its proof, followed by discussions on mapping moduli spaces, isomorphisms, and resolutions. Investigate filtrations, including action filtration, and the PSS map. This talk, part of the IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry series, offers a comprehensive exploration of cutting-edge research in symplectic geometry and related fields.