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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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Gabor Pataki, Geometric Methods in Representation Theory Seminar

March 31 @ 4:40 pm - 5:40 pm

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…

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April 2017

Almut Burchard (Univeristy of Toronto), Analysis Seminar

April 5 @ 2:00 pm - 3:00 pm

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.

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Dmitri Burago (Penn State University), Colloquium

April 6 @ 4:00 pm - 5:00 pm

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…

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

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

Title:  TBA Abstract:  TBA

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Vassily Gorbounov (University of Aberdeen), Physically Inspired Mathematics

April 11 @ 4:00 pm - 5:00 pm

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…

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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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Andrew Stuart (), Analysis Seminar

April 12 @ 4:00 pm - 5:00 pm

Title:  TBA Abstract:  TBA

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John Toth (), Analysis Seminar

April 19 @ 4:00 pm - 5:00 pm

Title:  TBA Abstract:  TBA

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