Some translation surfaces are examples of compact surfaces of genus ≥2 equipped with a metric that is flat everywhere except at finitely many cone points that have angle greater than 2π. When possible, we avoid geodesics that avoid cone points (the singular set) and use the hyperbolicity introduced by the cone points. We show that that sufficiently regular potential functions have unique equilibrium states if the singular set does not support the full pressure. I plan to talk about some of the tools we use and give an overview of why this is interesting to think about.
Uniqueness of Equilibrium States for Geodesic Flow on Translation Surfaces
Noelle Sawyer, Southwestern UniversityAuthors: Benjamin Call, David Constantine, Alena Erchenko, Noelle Sawyer, and Grace Work
2022 AWM Research Symposium
Women in Groups, Geometry, and Dynamics