Appears on: Mathematics
Research Focus
I study symplectic geometry, the natural geometry of classical and quantum mechanics, where coordinates come in pairs corresponding to position and momentum. Replacing "phase spaces" with more abstract "symplectic manifolds," the laws of physics translate into a way to measure 2-dimensional areas. I study problems at the interface of symplectic geometry, algebraic geometry, and discrete geometry. Most recently, I have been trying to identify and quantify the essential features of a symplectic structure and of the symmetries that preserve such a structure. With my collaborators, I have uncovered intriguing patterns in the quantitative data arising in our investigations. We have been able to verify a number of these patterns and there remain many open questions.
Publications
(selected)
- On infinite staircases in toric symplectic four-manifolds (with Daniel Cristofaro-Gardiner, Alessia Mandini, and Ana Rita Pires), J. Diff. Geom. 129 (2025) no.2, 335–413.
Equivariant cohomology does not distinguish Hamiltonian S1-manifolds (with L. Kessler), Adv. Math. 480 (2025), part B, Paper No. 110497, 108 pp.
The equivariant cohomology of complexity one spaces (with L. Kessler), L’Enseignement Mathématique, 65 (2019) no. 3-4, 457–485.
- 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.
In the news
- Celebrating April as Mathematics Awareness Month
- Banerjee named Mellon Fellow in diversity network
- Math communicator visits campus to explore math in everyday life
- Active Learning Initiative, at 10, elevates teaching and belonging
- arXiv hits 2M submissions
- Robert Strichartz, math analyst, dies at 78
- Cornell mathematicians featured at International Congress of Mathematicians
- Active learning helps math department boost academic success
- Shapes, Floppy and Squeezable
- Cook Awards honor those committed to women's issues
- $2.7 million grant expands Arts & Sciences Active Learning Initiative