Maseeh Mathematics + Statistics Colloquium Series

Speaker: Dr. Elizabeth Field,
Department of Engineering & Mathematics, University of Washington Bothell

Title: End-periodic homeomorphisms and volumes of mapping tori

Abstract: In this talk, we will explore 3-manifolds which arise as mapping tori of surfaces whose fundamental groups are infinitely generated. We will begin with an introduction to the world of these infinite-type surfaces. From there, we will introduce the notion of an end-periodic homeomorphism. We will then explore how the geometry of the associated mapping torus is related to certain topological and dynamic features of the end-periodic gluing map. In particular, we will see how the hyperbolic volume of the 3-manifold can be bounded above and below in terms of a certain dynamical feature of the homeomorphism. This talk represents joint work with Autumn Kent, Heejoung Kim, Christopher Leininger, and Marissa Loving (in various configurations).

Biography: Dr. Elizabeth Field is an Assistant Professor in the Department of Engineering & Mathematics at the University of Washington Bothell. She received her PhD from the University of Illinois at Urbana-Champaign under the supervision of Ilya Kapovich in 2020. After graduating, she worked for four years as a postdoc at the University of Utah. Her research lies in the fields of geometric group theory and low-dimensional topology, with a particular interest in hyperbolic groups and their boundaries, automorphisms of free groups, mapping class groups, and surfaces and 3-manifolds.

PSU faculty host: Dr. Steven Bleiler