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Super A-Polynomials: the Quantized and Categorified Knot InvariantsGeometry/Topology
|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.