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.

## Presentations

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

## Papers

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

## Notes

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