April 12, 4:00 p.m. – 5:00 p.m.
Ruane Center for the Humanities LL05
Unknotting the Knotty Notion of Knots (and their finite type invariants)
Robyn Brooks, Ph.D.
Boston College
Knot theory is the mathematical study of knots: simple closed curves in 3-D Euclidean space. One of the main goals of knot theory is to determine when two knots are equivalent: when one knot can be transformed into the other, by deformations that do not involve cutting or self-intersection of the “string”. Often, invariants from topology are used to determine if two knots are equivalent. In this talk, I will introduce the mathematical ideas behind knot theory, and show how knots may be represented as projections (plane diagrams). I will then talk about a particular group of knot invariants, called invariants of finite type. I will explain how one may compute the value of a finite type invariant from a regular knot plane diagram. This is done by using a Gauss diagram formula – a formula which counts certain sub-diagrams of crossings within a plane diagram. I will then talk about my research, which looks to extend these formulae to plane diagrams which are not regular – in particular, to plane diagrams which may have triple or other higher order crossings.
Professor Robyn Brooks is a Visiting Assistant Professor at Boston College, and does research in Algebraic and Computational Topology. As a mathematician, she is interested in: engaging in and collaborating on interesting math problems with people who value her as a human and mathematician, teaching students mathematics in a way that centers their humanity, engages them intellectually, and inspires their mathematical creativity, and working to erase outdated norms in academia that lead to discrimination, with the goal of making mathematics a field which allows on to be a fully-rounded, happy, and successful person. When she is not thinking about math, she likes to quilt, and take her dog Zelda on long walks.
If you are a person with a disability and require an assistive device, service, or other accommodation to participate in this event, please contact the Central Reservations Coordinator (401-865-2070; M-F 8:30a.m. – 4:30p.m.) well in advance of this event.
