The Arc-Floer conjecture for isolated hypersurface singularities

Let $f \in \mathbb{C}\{z_0,\dots,z_n\}$ be a convergent power series such that $f(\mathbf{0})=0$ that defines an isolated hypersurface singularity at the origin. For every integer $m\geq 1$, let $\mathcal{X}_m$ be the $m$-th restricted contact locus of $f$, let $\mathbb{F}$ be the Milnor fiber, and let $\varphi:\mathbb{F}\to\mathbb{F}$ be its compactly supported exact monodromy. Arc-Floer conjecture. There is an isomorphism

$$H_c^{\bullet+n(2m+1)}(\mathcal{X}_m,\mathbb{Z}/2\mathbb{Z})\cong \mathrm{HF}_\bullet(\varphi^m,+).$$

This conjecture proposes a direct correspondence between the algebraic geometry of restricted contact loci and the symplectic topology of Milnor fibers. It was previously known in particular when $m$ equals the multiplicity of $f$, and the paper proves it for plane curves; the general isolated-hypersurface case remains open.