CCMS Colloquium: Braids, Polynomials, and Hilbert’s 13th Problem (Jesse Wolfson, UC Irvine)

Speaker:Jesse Wolfson, UC Irvine

Title: Braids, Polynomials, and Hilbert’s 13th Problem

Abstract: There are still completely open fundamental questions about polynomials in one variable. One example is Hilbert’s 13th Problem, a conjecture going back long before Hilbert. Indeed, the invention of algebraic topology grew out of an effort to understand how the roots of a polynomial depend on the coefficients. The goal of this talk is to explain part of the circle of ideas surrounding these questions. Along the way, we will encounter some beautiful classical objects – the space of monic, degree d square-free polynomials, algebraic functions, lines on cubic surfaces, level structures on Jacobians, braid groups, Galois groups, and configuration spaces – all intimately related to each other, all with mysteries still to reveal. This is ongoing joint work with Benson Farb and Mark Kisin.

Bio: Jesse Wolfson is an associate professor and vice chair of inclusive excellence in the department of mathematics at the University of California, Irvine.  His research focuses on long-standing open problems at the interface of algebra, geometry and topology.  His perspective on geometry and topology emerges in part from his long-running exchange with choreographer Reggie Wilson. He currently serves on the board of directors of Wilson’s Fist and Heel Performance Group, an internationally acclaimed Brooklyn based “Post-African neo-hoodoo modern dance company.”