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## 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 »## Dmitri Burago (Penn State University), Colloquium

Tea at 3:30 pm in 330 Phillips Hall Title: A relaxed discussion of several problems involving Geometry, Dynamics, PDEs, Discretization, Control Theory and such. Abstract: The lecture consists of several mini-talks with just definitions, motivations, some ideas of proofs, and open problems. I will discuss some (hardly all) of the following topics. Or something else:) 1. “A survival guide for feeble fish”. How fish can get from A to B in turbulent waters which maybe much fasted than the locomotive speed of the fish (provided that…

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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