Knot Homologies and BPS States: April 22-April 28, 2012

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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.


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 & Slides

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