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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 »## Gabor Pataki, Geometric Methods in Representation Theory Seminar

Title: Combinatorial characterizations in semidefinite programming duality Abstract: I will discuss optimization problems over affine slices of positive definite symmetric matrices. These problems, called semidefinite programs (SDPs), have numerous applications. Several basic properties of SDP's are rooted in the fact that the linear image of the cone of symmetric positive semidefinite matrices may not be closed. Examples of these properties include the non-triviality of the infeasibility problem (when the set of positive semidefinite matrices has an empty intersection with an affine subspace) and pathological properties of dual SDP's. In this…

Find out more »## Almut Burchard (Univeristy of Toronto), Analysis Seminar

Title: On a non-local shape optimization problem related with swarming Abstract: I will discuss recent work with Rustum Choksi and Ihsan Topaloglu on a shape optimization problem where the energy functional is given by an attractive/repulsive interaction potential in power-law form. A natural conjecture is that balls minimize this energy for large mass, and minimizers fail to exist if the mass falls below a certain critical threshold. We have partial results that support this view.

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 »## Vassily Gorbounov (University of Aberdeen), Physically Inspired Mathematics

Title: New feature of the Schubert calculus Abstract: In the talk we will describe a new feature of the Schubert calculus in the equivariant cohomology or K theory which holds for all types of the classical Lie groups. As the main example we will use the torus equivariant cohomology and the type A Grassmanians. The usual definition of the Schubert cycles involves a choice of a parameter, namely a choice of a full flag. Studying the dependence of the construction of…

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

Title: TBA Abstract: TBA

Find out more »## Andrew Stuart (), Analysis Seminar

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Find out more »## John Toth (), Analysis Seminar

Title: TBA Abstract: TBA

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