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.
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. More particularly, some of her more recent work on rewriting systems for groups and semigroups also has close connections to the study of Groebner bases for commutative and noncommutative algebras.
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.
Nathan Corwin Collin Bleak and John Orr
Melanie DeVries Mark Brittenham and Susan Hermiller
Scott Dyer Mark Brittenham and Susan Hermiller
Muhammed Inam John Meakin
Ashley Johnson Mark Brittenham and Susan Hermiller
Anisah Nu'man Mark Brittenham and Susan Hermiller