Knot Homologies and BPS States (2012)
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.
-
Participants
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
- Mikhail Khovanov
Link Homology for Tangles and Cobordisms - Lev Rozansky
Khovanov Homology of a Unicolored B-adequate Link Has a Tail - Mina Aganagic
Refined Chern-Simons Theory, Topological Strings and Knot Homology (PDF) - Ivan Cherednik
Hyperpolynomials of torus knots via DAHA (PDF)
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
- Hiraku Nakajima
AGT Conjecture, perverse sheaves on instanton moduli and what I learned this week (PDF) - Yan Soibelman
Motovic Donaldson-Thomas Invariants, Hall Algebras & Knot Invariants - Andrew Neitzke
Spectral Networks - Robbert Dijkgraaf
Topological Strings, Quantum Curves, and Knot Invariants
- Mikhail Khovanov