Geometry and Topology Seminar: Resolvent degree via special points

Abstract: The theory of resolvent degree draws from from Klein's "hypergalois" program and broader industries of reducing numbers of coefficients, having developed into an invariant measuring the complexity of algebraic functions, field extensions, groups, and moduli problems. We offer a concrete introduction to RD through focusing on finite groups, emphasizing the notion of versality paradigmatic of Klein's program. We also discuss the general framework implemented in joint work with Alexander Sutherland and Jesse Wolfson, building on those of Farb–Kisin–Wolfson and Duncan–Reichstein, that permit us to address resolvent questions via classical invariant theory in new ways. We will conclude by reflecting on the rich history of solving polynomials, along with what we do and don't know about RD.

Host: Rachel Roberts