End-periodic homeomorphisms and volumes of mapping tori

In this talk, I will discuss the geometry of mapping tori which arise from end-periodic homeomorphisms of infinite-type surfaces. In particular, I will give bounds on the hyperbolic volume of these 3-manifolds in terms of the dynamics of the end-periodic map. I will show how the upper bound on volume utilizes tools of subsurface projections and the geometry of the curve complex. I will also discuss the lower bound on volume, which relies on the machinery of pleated surfaces, suitably adapted to our setting of infinite-type surfaces. This talk represents joint work with Autumn Kent, Heejoung Kim, Chris Leininger, and Marissa Loving (in various configurations).