Knots in Washington XLI: a Conference Series on Knot Theory and its Ramifications; November 13-15, 2015

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There will be six conferences over the next three-year period. This is a continuation of a very successful conference series "Knots in Washington", with a conference held every semester in the greater Washington DC area since Fall 1995. The first conference funded under this grant (and the 51st conference in the series) will be held in Fall 2015. The series will provide opportunity for researchers in the area to share their latest ideas and to collaborate with each other. The presentations will include plenary talks by distinguished researchers, as well as short talks by various participants. Graduate students and recent PhDs will also be encouraged to attend. Over the years, we have attracted a large number of postdocs, graduate students, and even some undergraduate students. In the greater Washington DC area, the series helps to bring together the relevant researchers, and to boost research activities in the region. Internationally, "Knots in Washington" has attracted researchers from all over the world, and is now considered 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 that will be suitable for research mathematicians, students, and readers with background in other exact sciences, including physics, computer science, biology, and chemistry. The next conference will focus on the connections between Khovanov homology, homology of distributive structures, Yang-Baxter homology, and Quantum Computing, as well as on the general idea of categorification, including categorification of skein modules. There have been exciting new developments in the area of knot theory and 3-manifold topology in the last 35 years -- from 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, 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 will provide a place for researchers in the above mentioned areas to communicate with each other and work together. The organizers will strive to be at the frontier of new developments in knot theory and its ramifications. Distinguished researchers will give plenary talks surveying the state of knowledge related to Khovanov homology. The choice of conference topics will also reflect the strength of the topology group at the George Washington University. Conference Web Page: http://home.gwu.edu/~przytyck/knots/index.html