Research

My research is in dynamics--the mathematical study of systems that change over time. I am also interested in differential geometry and topology, and especially in how dynamics are generated or restricted by the underlying geometry or topology of a space. Two dynamical systems that I have spent a lot of time thinking about are geodesic flows and convex billiards.

Notes and Talks

• Franks' lemma in geometric contexts.
  Slides from a talk at the Workshop for Dynamical Systems at Penn State (October, 2011).
• The Teetotaler's Tour: A Simple Strategy for the Aspiring Globetrotter
  A colloquium talk given at Hope College (January, 2011).
• Groups of polynomial growth
  Partial notes on Gromov's 1981 paper of the same title (March, 2009).
• Cohomological equations in dynamical systems
  Notes from a talk for the NU graduate student seminar (October, 2008).

Research Papers

• Minimal Free Resolutions of Complete Bipartite Graph Ideals
  Comm. Algebra 34 (2006), no. 10, 3761--3766.
• Presentations and Representations of Metacyclic Groups
  with D. Banu, J. Langford. Hope College Summer REU (2005).

  This research was expanded and published by the following REU group in:
  A. Heald, M. Pearson, M. Zaremsky. Waffles: Irreducible Representations of Metacyclic Groups.
  Pi Mu Epsilon J. 13 (2010), no. 2, 93--104.