Date & Time: Wednesday, August 5, 2015, 16:00-17:00.
Venue: Ramanujan Hall
Speaker: Abhijit Champanerkar, College of Staten Island and The Graduate Center, CUNY
Title: Density spectra for knots
Abstract: Knot theory has a fascinating history of using techniques from diverse fields of mathematics. In this talk we will explore the interactions of knot theory, hyperbolic geometry and graph theory. We study two natural quantities: the volume density defined as the hyperbolic volume of a knot complement per crossing number, a geometric invariant, and the determinant density defined similarly, a diagrammatic invariant. We will talk about recently discovered interesting relationships between the spectra of volume and determinant densities, and explore natural questions motivated by these bounds. The techniques used in answering some of these questions involve an interesting blend of graphs, dimer models and circle packings, in addition to geometric techniques such as polyhedral decomposition and volume bounds. This is joint work with Ilya Kofman and Jessica Purcell.