Tara Holm

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.