**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.