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March 2017

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

March 24 @ 4:00 pm - 5:00 pm

Title:  TBA Abstract:  TBA

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Mikhail Khovanov (Columbia University), Brauer Lectures

March 29 @ 3:30 pm - 4:30 pm

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.

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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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April 2017

Chuan-Hua Chen (Duke University), Applied Mathematics Colloquium

April 7 @ 4:00 pm - 5:00 pm

Title:  TBA Abstract:  TBA

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William Minicozzi (), PDE Minischool

April 12 @ 8:00 am - April 13 @ 5:00 pm

Title:  TBA Abstract:  TBA

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Prof. Elon Lindenstrauss (Hebrew University of Jerusalem), Colloquium

April 20 @ 4:00 pm - 5:00 pm

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

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Amanda Randles (Duke University), Applied Mathematics Colloquium

April 21 @ 4:00 pm - 5:00 pm

Title:  TBA Abstract:  TBA

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