Knots in Washington XVIII: Khovanov homology

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AbstractAward: DMS-0432284Principal Investigator: Jozef H. PrzytyckiThis award provides partial participant support for the 18thconference in the series, "Knots in Washington." This meeting isdevoted to the theme of Khovanov homology, and aims to bringexponents of that new theory together with recent and currentstudents in topology, along with experienced researchers in otheraspects of knot theory and quantum topology.A large number of methods have been developed for computingnumbers or polynomials that each measure some aspect of thecomplexity of a knotted curve in space. The Alexanderpolynomial, which is approximately 70 years old, is the firstexample of this powerful class of tools. The search forsharper ways to distinguish one knot from another and tounderstand associated geometric questions gathered speedapproximately 20 years ago with the discovery of the Jonespolynomial and related invariants. Mikhail Khovanov of theUniversity of California, Davis, found in 1999 that the Jonespolynomial can be viewed as a one-line summary of a richertheory, and ongoing work with Khovanov's ideas will be thetheme of this conference.