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
Ellyn Collier
Mark Brittenham
Ash DeClerk
Susan Hermiller
Audrey Goodnight
Mark Brittenham and Susan Hermiller
Aurora Marks
Mark Brittenham and Susan Hermiller
Nick Meyer
Alex Zupan
Andrew Quaisley
Mark Brittenham and Susan Hermiller
Kaitlin Tademy
Mark Brittenham
Kathryn Van Etten
Susan Hermiller
Ana Wright
Mark Brittenham and Alex Zupan
Recent Graduates
Jesse Moeller (PhD 2021)
Mark Brittenham and Alex Zupan
Vince Longo (PhD 2021)
Mark Brittenham and Alex Zupan
Robert Huben (PhD 2021)
Mark Brittenham and David Pitts
Marla Williams (PhD 2020)
Mark Brittenham and Alex Zupan
Katie Tucker (PhD 2019)
Mark Brittenham and Susan Hermiller
Corbin Groothius (PhD 2018)
John Meakin and Jamie Radcliffe
Maranda Franke (PhD 2017)
Mark Brittenham and Susan Hermiller
Muhammed Inam (PhD 2016)
Mark Brittenham and John Meakin
Nicholas Owad (PhD 2016)
Mark Brittenham and Susan Hermiller
Scott Dyer (PhD 2015)
Mark Brittenham and Susan Hermiller
Anne Kerian (PhD 2015)
Mark Brittenham
Anisah Nu'man (PhD 2015)
Mark Brittenham and Susan Hermiller
Nathan Corwin (PhD 2013)
Collin Bleak and Mark Brittenham
Melanie DeVries (PhD 2013)
Mark Brittenham and Susan Hermiller
Ashley Johnson (PhD 2013)
Mark Brittenham and Susan Hermiller