Geometry MMA Seminar: Counting fixed points of pseudo-Anosov maps

Speaker:   David Futer,Temple University 

Title:   Counting fixed points of pseudo-Anosov maps

Abstract:  Let S be a hyperbolic surface and f a pseudo-Anosov map on S. I will describe a result (joint with Tarik Aougab and Sam Taylor) that predicts the number of fixed points of f, up to constants that depend only on the surface S. If f satisfies a mild condition called “strongly irreducible,” then the logarithm of the number of fixed points of f is coarsely equal to its translation length on the Teichmuller space of S. Without this mild condition, there is still a coarse formula.

This result has some applications to the search for surface subgroups of mapping class groups, and to relations between the hyperbolic volume and the knot Floer invariants of fibered hyperbolic knots.

Time: Monday, February 26, 2024 – 10:30am-11:30am

Place: Exploratory Hall, Room 4106