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March 2017

Mikhail Khovanov (Columbia University), Brauer Lectures

March 30 @ 3:30 pm - 4:30 pm

Lecture 2 Title: Categorifications of quantum link invariants   Abstract: The Jones polynomial has many generalizations, including the two-variable HOMFLYPT polynomial. We will review approaches to the categorification of the HOMFLYPT polynomial and its specializations. Several new ideas proved crucial, including evaluating foams (two-complexes embedded in 3-space) via systems of Frobenius algebras that come from cohomology rings of flag varieties and constructing functorial tangle invariants via matrix factorizations. Matrix factorizations are generalized complexes with the square of the differential equal…

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Mikhail Khovanov (Columbia University), Brauer Lectures

March 31 @ 3:30 pm - 4:30 pm

Lecture 3 Title: Categorification of quantum groups at generic q and at a root of unity   Abstract: Quantum link invariants naturally emerge from actions of quantum groups on tensor powers of their irreducible representations. Categorifications of quantum groups and how they fit into link homology theories will be explained. Categorified quantum groups act on many categories of interest in representation theory and adjacent fields. The quantum parameter q, in the generic situation, becomes a grading shift upon categorification. For…

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