Jiahui Huang, Department of Pure Mathematics, University of Waterloo
"Arc-Floer conjecture"
For a hypersurface singularity, the arc-Floer conjecture states an isomorphism between the compactly supported cohomology of $X_m$, the m-th restricted contact locus (of algebraic nature), and the Floer homology of $\varphi^m$, the m-th iterate of the monodromy on the Milnor fiber (of topological nature). In particular, this gives the Floer homology a mixed Hodge structure.
It was known by a result of Denef and Loeser that the Euler characteristic of $X_m$ agrees with the Lefschetz number of $\varphi^m$, which is given by the Euler characteristic of its Floer homology. The conjecture predicts an equivalence at the level of cohomology. It has been proven for plane curves by de la Bodega and de Lorenzo Poza. We shall look at the case where the singularity is the affine cone of a smooth projective hypersurface.
MC 5417