Elizabeth Field

Assistant Professor

Location: DISC-352M
Email: ecfield@uw.edu

Background

Elizabeth Field received her B.A. in Mathematics from Southern Connecticut State University, where she also graduated with a B.S. in Elementary and Special Education. She completed her doctoral degree in Mathematics at the University of Illinois at Urbana-Champaign. She went on to work at the University of Utah where she was a NSF Postdoctoral Scholar. Her research interests are in geometric group theory, geometric topology, and low-dimensional topology.

Research

Field’s current research projects lie primarily in the intersection of the fields of geometry, topology, and algebra. While geometry is concerned with rigid properties of spaces, such as distance and measurements, topology focuses on properties of spaces that remain unchanged when the space is deformed via actions such as twisting, stretching, or shrinking. In one ongoing research project, Field studies topological spaces which include 2-dimensional surfaces (think of the glaze on a donut – this is an example of a surface with one “hole”, known as a torus) and 3-dimensional manifolds. It turns out that certain 3-manifolds can be built from surfaces utilizing a symmetry of the surface and then given a geometry which depends on the symmetry used in the construction. With this geometry, one can then ask questions about the volume of the resultant 3-manifold. Field studies the relationship between the volume of the 3-manifold and the symmetry of the surface used in the construction and uses tools from algebra to formalize these relationships.

Courses

• MATH 300 Foundations of Modern Math
• MATH 441 Topology

Education

University of Illinois at Urbana-Champaign – Champaign, IL
Ph.D. – Mathematics

Southern Connecticut State University – New Haven, CT
B.A. – Mathematics
B.S. – Elementary and Special Education