The focus of my research is knot theory and geometric topology.  Knot theory is one of the most active research areas of mathematics today. Much of this research is closely connected with mathematical physics, and many results are of interest to biologists.  For such a rich field of mathematical ideas, the "price of admission" is low for great undergraduate research projects.

My current research is motivated by a deep open problem: how to bridge the chasm between quantum and geometric topology.  Thurston established the importance of geometric invariants, especially hyperbolic volume, in low-dimensional topology.  A revolution in knot theory was ushered in with the discovery of the Jones polynomial in 1984, which led to vast families of quantum invariants.  My aim is to establish the relationship between quantum invariants of a knot, such as the Jones polynomial, and the geometry of the knot complement