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I study symplectic geometry and its relationships with combinatorics, algebraic topology, and algebraic geometry. Recent projects include: (1) investigating origami structures: structures which are nearly but not quite symplectic; (2) exploring the topology of symplectic quotients that are orbifolds; and (3) computing symplectic invariants such as the Gromov width.
- The topology of toric origami manifolds (with Ana Rita Pires), Math. Research Letters, 20 no. 5 (2013), 885–906.
- Orbifold cohomology of torus quotients (with Rebecca Goldin and Allen Knutson), Duke Math. J. 139 no. 1 (2007), 89–139.
- Computation of generalized equivariant cohomologies of Kac-Moody flag varieties (with Megumi Harada and Andre Henriques), Adv. in Math. 197 no. 1 (2005), 198–221.
- Conjugation spaces (with Jean-Claude Hausmann and Volker Puppe), Algebr. Geom. Topol. 5 (2005), 923–964.
- Distinguishing chambers of the moment polytope (with Rebecca Goldin and Lisa Jeffrey), J. Symp. Geom. 2 no. 1 (2003), 109–131.