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headshot of Ross Geoghegan

Ross Geoghegan

Research Professor

Mathematical Sciences

Background

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”.

Education

  • BSc, MSc, University College, Dublin
  • PhD, Cornell University

Research Interests

  • Topology
  • geometric group theory
  • fixed point theory
  • dynamics

Awards

  • STAR Award for University Service

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