Areas of Interest
Geometric topology, Combinatorial group theory
Research
I am currently interested in the mathematical interactions of a collection of groups that arose first in logic and universal algebra. The groups are generalizations of three groups first discovered by Richard Thompson. The groups show up in a strong way in logic, homotopy and shape theory, dynamical systems, categorical algebra and its relation to physics, and the combinatorial group theory of the word problem and of infinite simple groups. They are a source of examples or potential examples in geometric group theory, cohomology of groups, string rewriting systems and abstract measure theory.
Ph.D. Students
-
Jeremy Hauze,
Fall, 2017
— Restrictions on potential automatic structures on Thompson's group F
-
Amanda Taylor,
Summer, 2017
— Locally solvable subgroups of PLo(I)
-
Bronlyn Wassink,
Spring, 2008
— Subgroups of R. Thompson's Group F that are Isomorphic to F
-
Olga Salazar-Diaz,
Spring, 2006
— Thompson's Group V From A Dynamical Viewpoint
-
Collin Bleak,
Summer, 2005
— Solvability in Groups of Piecewise Linear Homeomorphisms of the Unit Interval
-
Collin Bleak,
Summer, 2005
— Solvability in Groups of Piecewise Linear Homeomorphisms of the Unit Interval
-
John Donnelly,
Summer, 2003
— Properties of Richard Thompson's group F related to amenability
Notes
Edit this profile
