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## Steve Wise (University of Tennessee, Knoxville), Applied Mathematics Colloquium

Title: TBA Abstract: TBA

Find out more »## Mikhail Khovanov (Columbia University), Brauer Lectures

Overall title of the Brauer Lecture Series 2017: Link homology and categorification Lecture 1 Title: The Jones polynomial of links and tangles and its categorification. Abstract: The Jones polynomial is a celebrated invariant of links with roots in the representation theory of quantum groups and the Chern-Simons theory. It's a one-variable Laurent polynomial, and we will describe its lifting to a bigheaded link homology theory. Functoriality of the theory will be explained, together with several applications in low-dimensional topology.

Find out more »## Mikhail Khovanov (Columbia University), Brauer Lectures

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…

Find out more »## Mikhail Khovanov (Columbia University), Brauer Lectures

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…

Find out more »## Chuan-Hua Chen (Duke University), Applied Mathematics Colloquium

Title: TBA Abstract: TBA

Find out more »## William Minicozzi (), PDE Minischool

Title: TBA Abstract: TBA

Find out more »## Prof. Elon Lindenstrauss (Hebrew University of Jerusalem), Colloquium

Tea at 3:30 in 330 Phillips Hall Title: TBA Abstract: TBA

Find out more »## Amanda Randles (Duke University), Applied Mathematics Colloquium

Title: TBA Abstract: TBA

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