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Super A-Polynomials: the Quantized and Categorified Knot Invariants


Speaker: Piotr Sułkowski, California Institute of Technology (Physics) and University of Amsterdam
Location: 2112 MSB
Start time: Tue, Dec 4 2012, 3:10PM

We introduce a new knot invariant, the so-called super A-polynomial, and discuss some of its properties. The super A-polynomial of a given knot takes the form of an algebraic curve that depends on two deformation parameters, and generalizes the well known A-polynomial. From the mathematical point of view the super A-polynomial encodes information of the homological knot invariants. Physically it plays an important role in a large class of 3-dimentional N=2 supersymmetric theories (related by the 3d-3d duality to knots), which is analogous to the role of the Seiberg-Witten curve in 4-dimensional theories.