MAA NCS Spring 2025 meeting

Invited Speaker: Opel Jones (MAA – NAM Speaker)

Talk Title: Forthcoming

Talk Abstract:  Forthcoming

Invited Speaker: Claudio Gómez-Gonzáles (MAA NCS Section NExT Speaker, Carleton College)

Talk Title: How hard could it be? An invitation to resolvent degree

Talk 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. This overview makes contact with the origins of topology, miracles of classical algebraic geometry, Klein’s “hypergalois” program, and centuries-old exploits in reducing coefficients, which dare us to push beyond the solvable/unsolvable dichotomy. We will build towards the notion of versality central to Klein’s vision and, time permitting, allude to a general framework implemented in joint work with Alexander Sutherland and Jesse Wolfson that addresses resolvent questions via classical invariant theory. Throughout the talk, we will reflect on the past and future of resolvent problems, the value in grappling with hard questions even if we might not solve them, and what we do and do not know about RD. No background knowledge will be expected or required beyond calculus and linear algebra.