Principal Investigator: Jozef H. Przytycki
This award provides partial participant support for the 18th conference in the series, "Knots in Washington." This meeting is devoted to the theme of Khovanov homology, and aims to bring exponents of that new theory together with recent and current students in topology, along with experienced researchers in other aspects of knot theory and quantum topology.
A large number of methods have been developed for computing numbers or polynomials that each measure some aspect of the complexity of a knotted curve in space. The Alexander polynomial, which is approximately 70 years old, is the first example of this powerful class of tools. The search for sharper ways to distinguish one knot from another and to understand associated geometric questions gathered speed approximately 20 years ago with the discovery of the Jones polynomial and related invariants. Mikhail Khovanov of the University of California, Davis, found in 1999 that the Jones polynomial can be viewed as a one-line summary of a richer theory, and ongoing work with Khovanov's ideas will be the theme of this conference.
