Claremont Topology Seminar: Claudio Gomez-Gonzales (Carleton College – UC Irvine)

We welcome all undergraduate/graduate students and faculty to attend the Topology Seminar!

Speaker: Claudio Gomez-Gonzales (Carleton College – UC Irvine)

Title: How hard could it be? A tour of resolvent degree

Abstract: Solving algebraic equations are among the oldest problems in mathematics. In this talk, we offer a concrete, visual, and historical introduction to resolvent degree (RD), an invariant that aspires to quantify just how hard these problems are. The lineage of this theory includes the origins of topology, Klein’s “hypergalois” program, and centuries-old exploits in reducing numbers of coefficients, which dare us to push beyond the solvable/unsolvable dichotomy. We will build towards the notion of versality central to Klein’s vision, with a nod to our general framework implemented in joint work with Alexander Sutherland and Jesse Wolfson, that permits us to address resolvent questions via classical invariant theory. We will conclude by reflecting on the past and future of resolvent problems, along with what we do and don’t know about RD. This talk is designed to be accessible for undergraduates—let’s do some math!