Groups Semigroups and Topology

The interplay between topology, group theory, and semigroup theory has yielded a wealth of information in all three mathematical fields. These connections are central to the research of our faculty working in this area.

Faculty

Mark Brittenham works in low-dimensional topology, a subject that focuses on spaces that have small dimension, such as surfaces, and knots (and their complements) in 3-space. His research involves studying surfaces in 3-dimensional manifolds, and the extent to which such surfaces can be used to reveal the structure of the manifold containing them. Depending upon the problem, the techniques involved can be combinatorial (using triangulations and `normal' surfaces), geometric (using hyperbolic geometry and foliation theory), or algebraic (using group actions and fundamental groups).

Susan Hermiller works in geometric group theory, which centers on the study of groups that can be viewed as nonpositively curved topological spaces. Her research interests include both the topological and computational/algorithmic properties of infinite groups. Her work on rewriting systems for groups also has close connections to the study of Groebner bases for commutative and noncommutative algebras..

Alex Zupan's research is in geometric topology, low-dimensional topology, and knot theory.

Emeritus Professor John Meakin has research interests in semigroup theory and geometric group theory. Some of his particular interests are in the theory of inverse semigroups (essentially semigroups of partial symmetries of mathematical objects) and in the study of algorithmic problems in semigroup theory and infinite group theory. His work uses geometric and topological techniques as well as ideas from automata theory, formal language theory, and mathematical logic.

Current Graduate Students

Maranda Franke
Mark Brittenham and Susan Hermiller

Katie Tucker
Mark Brittenham and Susan Hermiller

Marla Williams
Alex Zupan and Mark Brittenham

Recent Graduates

Nathan Corwin (PhD 2013)
Collin Bleak and Mark Brittenham

Melanie DeVries (PhD 2013)
Mark Brittenham and Susan Hermiller

Scott Dyer (PhD 2015)
Mark Brittenham and Susan Hermiller

Muhammed Inam (PhD 2016)
Mark Brittenham and John Meakin

Ashley Johnson (PhD 2013)
Mark Brittenham and Susan Hermiller

Anne Kerian (PhD 2015)
Mark Brittenham

Anisah Nu'man (PhD 2015)
Mark Brittenham and Susan Hermiller

Nicholas Owad (PhD 2016)
Mark Brittenham and Susan Hermiller