My mathematical interests are primarily in geometry. The field of study for my doctoral research was differential geometry –  specifically, Hamiltonian actions in symplectic geometry and complex generalized geometry. My recent research projects have primarily been motivated by work with students, although most of it still involves geometric ideas – (see the Student Research tab above).

Most of the material below was produced while I was in graduate school, but I will update as I am able.


  1. The pigeonhole principle, Quantitative Reasoning course, Marymount Manhattan College, 14 April 2010, [slides]
  2. Bicycle math, Math, Computer Science, & Physics Seminar, Bard College, 1 April 2010, [slides]
  3. Bicycle math, Olivetti Seminar, Cornell University, 30 March 2010, [poster], [slides]
  4. Hamiltonian actions on integral Kähler manifolds, Mathematics Department Colloquium, Georgie Southern University, 6 November 2009.
  5. A little taste of symplectic geometry, Mathematics Seminar, Richard Stockton College, 19 October 2009, [slides].
  6. Hamiltonian actions in generalized complex geometry, Lie Groups Seminar, Cornell University, 25 September 2009, [notes].
  7. Groups, groupoids, and symmetry, Student Seminar, Union College, 22 April 2009, [slides].
  8. What’s purple and commutes, and ends with “oid”?, Olivetti Seminar, Cornell University, 24 February 2009, [poster].
  9. A convexity theorem for the real part of a Borel invariant subvariety, contributed paper, 2009 Joint Mathematics Meetings, Washington, DC, 5 January 2009, [slides].
  10. What is a connection, and what is it good for?, Olivetti Seminar, Cornell University, 1 April 2008, [notes].
  11. How to describe a moment polytope using a line bundle, Lie Groups Seminar, Cornell University, 15 February 2008, [slides].
  12. Convexity theorems from positive Hermitian line bundles, Lie Groups Seminar, Cornell University, 2 November 2007.
  13. The nonabelian convexity theorem, unofficial Bernstein Seminar, Cornell University, 19 October 2007.
  14. A little taste of symplectic geometry, Olivetti Seminar, Cornell University, 4 October 2007, [poster], [slides].
  15. A little taste of symplectic geometry, Math and CS Seminar, Bard College, 2 May 2007, [handout].
  16. Good news, everyone! Group actions, torsors, and affine space, Olivetti Seminar, Cornell University, 29 August 2006, [poster].
  17. A little Lie algera cohomology, if you please, Olivetti Seminar, Cornell University, 31 January 2006, [poster].
  18. The Lie bracket and the commutator of flows, Olivetti Seminar, Cornell University, 25 October 2005, [notes], [poster image].


  1. A convexity theorem for the involution fixed set of a Borel invariant subvariety, Proc. Amer. Math. Soc. 137 (2009), 1447-1458, arXiv:0709.3287v3.
  2. Combinatorial Laplacians of Simplicial Complexes, Senior Thesis, Bard College, May 2002, [pdf].


  1. The very, very basics of Hamiltonian actions on symplectic manifolds, 12 March 2009, [pdf].
  2. The symplectic integrability condition, answering what the closed condition of a symplectic form means, 3 September 2008, [pdf].
  3. About Lie groups, some notes about Lie groups, 23 April 2008, [pdf].
  4. About connections, some (unpolished and incomplete) notes about connections from my Olivetti talk, 1 April 2008, [pdf].
  5. The orientation manifesto (for undergraduates), some notes on orienting manifolds, 11 November 2007, [pdf].