Principal Investigator: Jozef H. Przytycki, Valentina S. Harizanov, Alexander N. Shumakovitch, Hao Wu
This award provides partial support for participants of a series of conferences devoted to knot theory and its ramifications. It is a continuation of the very successful series of the ``Knots in Washington'' conferences held every semester in the greater Washington, DC area since the Fall of 1995. This proposal asks for support for four conferences over the next three years. The first such conference is expected to be held in Fall of 2011, focusing on connections between Khovanov homology, homology of multi-shelves (e.g. quandles or Boolean algebras), and Quantum Computing, and relating to the general idea of categorification including categorification of skein modules. It will be the 33rd conference in the Knots in Washington Conference Series. There have been exciting new developments in the area of knot theory and 3-manifold topology in the last 30 years. From the Jones polynomial and quantum invariants of 3-manifolds, through Vassiliev invariants, topological quantum field theories, to relations with gauge theory type invariants in 4-dimensional topology (e.g. Donaldson, Witten). More recently, again, a new development in quantum topology has emerged in the form of ``Khovanov homology", a generalization of the Jones type polynomials to homology of chain complexes that significantly generalizes the invariants. Also, the categorification of the Kauffman bracket skein module of 3-manifolds has been proposed and developed for some manifolds. The relation to Hochschild homology of algebras has been discovered and studied. The (quantum) complexity of computing the Jones polynomial and Turaev-Viro invariants have been analyzed. "Knots in Washington" meetings would provide a place for researchers in described above areas to communicate and work with one another. Distinguished researchers will give plenary talks surveying the state of knowledge related to Khovanov homology. PhD students and fresh PhD's will be encouraged to attend. We strive to be always in the frontier of new developments in Knot Theory and its ramifications. Our choice of conference topics also reflects the strength of our topology group at the George Washington University.
Knots in Washington provides an opportunity for researchers in the area to share their latest ideas and to collaborate with each other. The presentations include plenary talks by distinguished researchers, as well as short talks by various participants. Over the years, we have attracted a large number of postdoctors, graduate students, and some undergraduates. In the greater Washington DC area, Knots in Washington helps to bring together the relevant researchers, and to boost the research activities in the region. Internationally, Knots in Washington has attracted researchers from all over the world, and is now considered as a major conference in knot theory and low-dimensional topology. We expect to publish conference proceedings (as we did in the past) containing cutting-edge research papers and lecture notes which will be suitable for research mathematicians, students and readers with background in other exact sciences, including biology, chemistry, computer science, and physics. Conference Web Page: http://home.gwu.edu/~przytyck/knots/index.html