Knot Homologies and BPS States (2012)

Date & Time

In recent years, homological knot invariants have been gaining momentum in both mathematics and physics, and recent developments promise it will only be growing. Therefore, a symposium on “the physics of knot homologies” is very timely.

Moreover, this subject is intimately connected with another active area of research at the interface of geometry and physics: the study of BPS invariants and their behavior under wall crossing. The relation between quantum invariants of knots and 3-manifolds on one hand, and wall crossing of refined BPS invariants on the other, is currently a very active area of research. The underlying reason for this interesting connection is that, in a physical realization of knot homologies as spaces of BPS states, the basic operations in knot theory (such as skein relations) correspond to changes of the (brane) system under which the spectrum of BPS states jumps.

  • Participantsplus--large

    Mina Aganacic UC Berkeley
    Ivan Cherednik University of North Carolina at Chapel Hill
    Robbert Dijkgraaf Universiteit van Amsterdam
    Davide Gaiotto Institute for Advanced Study
    Sergei Gukov California Institute of Technology
    Mikhail Khovanov Columbia University
    Peter Kronheimer Harvard University
    Ciprian Manolescu UCLA
    Hiraku Nakajima Kyoto University
    Andrew Neitzke University of Texas at Austin
    Alexei Oblomkov University of Massachusetts
    Andrei Okounkov Columbia University
    Hirosi Ooguri California Institute of Technology
    Peter Ozsvath MIT
    Jacob Rasmussen University of Cambridge
    Lev Rozansky Imperial College London
    Vivek Shende Princeton University
    Yan Soibelman Kansas State University
    Cumrun Vafa Harvard University
    Johannes Walcher CERN
  • Agenda & Slidesplus--large

    Monday, April 23

    Tuesday, April 24

    • Hirosi Ooguri
      Introduction and Overview by a Physicist
    • Cumrun Vafa
      Knot Homology, Mirror Symmetry & Topological Strings
    • Sergei Gukov
      What is Superpolynomial? (PDF)

    Wednesday, April 25

    • Alexei Oblomkov
      Khovanov-Rozansky homology, Hilbert schemes of points on planar curves and rational Cherednik algebras.
    • Vivek Shende
      Large N duality, singular curves, Hitchin fibres, and knot homology
    • Andrei Okounkov
      The Index & the Vertex

    Thursday, April 26

    • Ciprian Manolescu
      Knot Homologies and Tor Groups
    • Jacob Rasmussen
      DAHA and Differentials
    • Johannes Walcher
      On the Arithmetic of BPS states

    Friday, April 27

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