Let f be a pseudo-Anosov homeomorphism of a surface S with negative Euler characteristic. Under a mild assumption on f (which we can remove at the cost of a slightly more complicated theorem statement) we prove that the logarithm of the number of its fixed points grows like the translation length of f on the Teichmuller space. The proof utilizes techniques from veering triangulations, and we’ll explain some connections to knot floer homology and to constructing convex cocompact subgroups in the mapping class group.

This represents joint work with Dave Futer and Sam Taylor.