Quantum Topology / Hopf Algebra Seminar
Scott Baldridge
Loretta Cox Stuckey and Dr. James G. Traynham Distinguished Professor, Louisiana State University
A new cohomology for planar trivalent graphs with perfect matchings
Abstract: In this lecture, I will describe a simple-to-compute polynomial invariant of a planar trivalent graph with a perfect matching (think: Jones polynomial for graphs). This polynomial is interesting because of what it detects: If the polynomial is non-zero when evaluated at one, then the perfect matching is even. Such a perfect matching implies that the graph can be 4-colored. I will then show how to categorify this polynomial to get a Khovanov-like cohomology theory for planar trivalent graphs and compute a couple of simple examples. If time, I will talk about some consequences of the cohomology theory.
Thursday February 7, 2019 at 3:00 PM in 612 SEO