End-periodic homeomorphisms and volumes of mapping tori

Given an irreducible, end-periodic homeomorphism $f:S\to S$ of a surface with finitely many ends, all accumulated by genus, the mapping torus, $M_f$, is the interior of a compact, irreducible, atoroidal 3-manifold ${\overline{M}}_f$ with incompressible boundary. Our main result is an upper bound on the infimal hyperbolic volume of ${\overline{M}}_f$ in terms of the translation length of $f$ on the pants graph of $S$. This builds on work of Brock and Agol in the finite-type setting. We also construct a broad class of examples of irreducible, end-periodic homeomorphisms and use them to show that our bound is asymptotically sharp.