Research

A wise friend once said that each mathematician has in their heart a single problem or phenomena that animates their entire career. For me, this is (spaces of) configurations of points in the plane, i.e., (spaces of) polynomials. I am fascinated by the topology of enumerative problems. My current work is in resolvent degree, which is a centuries-old measure of complexity—formalized independently by Brauer (1975) and Arnold–Shimura (1976) and not officially named until Farb–Wolfson (2018)—that is motivated by one of our oldest and most important questions:

“How can we solve algebraic equations in the simplest manner possible?”

To learn more, see Sutherland’s dissertation and summary of known bounds, the seminal paper by Farb–Wolfson (also the associated Quanta article), and Reichstein’s recent overview. While you’re at it, check out Arnold’s retrospective where he casts his life’s work in pursuit of “essentially one problem” (and teaches us lots about math).