Areas of Interest
Topology, geometric group theory, fixed point theory, dynamics
Research
I am interested in the interplay between group theory and geometry/topology. In particular: geometric and homological group theory, fixed point theory, and certain parts of dynamical systems. Some of the questions motivating this work are algebraic, involving the algebraic K-theory of rings associated with the fundamental group; this is how I got interested in Nielsen fixed point theory, particularly parametrized versions of that theory. Other questions are about how an action by a discrete group on a non-positively curved space can lead to group theoretic information. I'm also interested in understanding the asymptotic topological invariants of a group. I have recently finished a book on that subject called "Topological Methods in Group Theory".
Ph.D. Students
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Ulysses Alvarez,
Spring, 2022
(Co-advisor:
Laura Anderson)
— On the topology of corank 1 tropical phased matroids
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Keith Jones,
Spring, 2010
— Controlled Connectivity for Cocompact Isometric Actions on Simplicial Trees
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Risto Atanasov,
Summer, 2007
— Groups of Geometric Dimension 2
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Tom Klein,
Spring, 2007
— Filtered ends of pairs of groups
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Nicholas Koban,
Spring, 2004
— Controlled Topology Invariants of Translation Actions
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Dirk Schuetz,
Spring, 2001
— Torsion properties of the Novikov complex
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Daniel Farley,
Spring, 2000
— Finiteness and CAT(0) Properties of Diagram Groups
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Tom Plavchak,
Fall, 1997
— A Polyhedral Transversality Theorem For One-Parameter Fixed Point Theory
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Francisco Fernandez-Lasheras,
Fall, 1996
— Fake surfaces, thickenings and cohomology of groups
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Mile Krajcevski,
January, 1995
(Co-advisor:
Craig Squier)
— Tilings of the plane, and hyperbolic groups.
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Michael Kelly,
May, 1985
— Minimizing the Number of Fixed Points for Self-Maps of Compact Surfaces
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Donco Dimovski,
Spring, 1983
— Non-Simply Connected Casson Handles
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Gary O'Brien,
Spring, 1981
— The Missing Boundary Problem for Smooth Manifolds of Dimension Greater Than or Equal to Six
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Michael Mihalik,
Spring, 1979
— Ends of Fundamental Groups in Shape and Proper Homotopy
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