I am interested most in the interplay of geometry, dynamical systems and Lie theory. In particular, my thesis was on rigidity phenomena for actions of lattice subgroups of semisimple Lie groups on compact smooth manifolds. (This is part of the Zimmer Program.) Lately, I have done some work with students in combinatorics on m-ary partition functions. As a post-doctoral instructor I also worked on a mathematical biology project.

If you are a student interested in pursuing mathematics research, please look over the list of student projects I have supervised.

Rigidity for actions of Lattices

  • with David Fisher, Cocycle Superrigidity and Harmonic Maps with Infinite-Dimensional Targets, International Mathematics Research Notices, vol. 2006, Article ID 72405, 19 pages, 2006.
  • with Alexander Gorodnik and Ralf Spatzier, Regularity of Conjugacies of Algebraic Actions of Zariski Dense Groups, Journal of Modern Dynamics, Vol 2, no 3, 507-538.
  • with David Fisher, Strengthening Kazhdan’s Property (T) by Bochner methods, Geometriae Dedicata, Vol 160, no 1, 333-364.
  • with David Fisher, Harmonic Maps into Infinite Dimensional Manifolds and Cocycle Superrigidity, in progress.

M-ary Partitions

  • with Mackenzie Roepke and James Sellers, Patterns in the Structure Polynomials for m-ary Partition Functions, in preparation.

Scholarship of Teaching and Learning

  • Euclidean Geometry: An introduction to Mathematical Work, to appear in the Journal of Inquiry Based Learning in Mathematics.
  • with Doug Shaw, Tailoring IBL Techniques to Liberal Arts Mathematics Classes without Losing Integrity or Quality, submitted 1 June 2013.
  • Running a Class Journal, submitted to MAA Notes volume on teaching proof writing, 15 July 2013.

Mathematical Modeling in Biology

  • with Robin Forman, Heather Hardway, Timothy Burke, and Diane Shao, Modeling the precision and robustness of Hunchback border during Drosophila embryonic development, Journal of Theoretical Biology, Volume 254, No. 2, 390-399.

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