Event Details - Topology Seminar

Kyle Hayden, Boston College

From algebraic curves to ribbon disks and back

Abstract: There is a rich, symbiotic relationship between knot theory and the study of algebraic curves in complex spaces. In particular, intersecting an algebraic curve in C^2 with a three-sphere of constant radius yields a knot or link that contains useful information about the algebraic curve. We'll look at a thirty-year-old conjecture about the relationship between different knots associated to the same algebraic curve. Using a simple construction, we'll show that the conjecture is false and that counterexamples are quite common.