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## March 2017

### 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 bigraded 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 »## April 2018

### Brauer Lecture: Dr. Mina Aganagic

The Alfred Brauer Lectures April 10 – 12, 2018 Dr. Mina Aganagic Professor of Mathematics and Physics, University of California, Berkeley Dr. Mina Aganagic is Professor of Mathematics and Physics at the University of California, Berkeley. She has a bachelor's degree and a doctorate from the California Institute of Technology, in 1995 and 1999 respectively. After a postdoctoral position at the Harvard University Physics Department and a faculty position at the University of Washington, she moved to UC Berkeley…

Find out more »### Brauer Lecture: Dr. Mina Aganagic

The Alfred Brauer Lectures April 10 – 12, 2018 Dr. Mina Aganagic Professor of Mathematics and Physics, University of California, Berkeley Dr. Mina Aganagic is Professor of Mathematics and Physics at the University of California, Berkeley. She has a bachelor's degree and a doctorate from the California Institute of Technology, in 1995 and 1999 respectively. After a postdoctoral position at the Harvard University Physics Department and a faculty position at the University of Washington, she moved to UC Berkeley…

Find out more »### Brauer Lecture: Dr. Mina Aganagic

The Alfred Brauer Lectures April 10 – 12, 2018 Dr. Mina Aganagic Professor of Mathematics and Physics, University of California, Berkeley Dr. Mina Aganagic is Professor of Mathematics and Physics at the University of California, Berkeley. She has a bachelor's degree and a doctorate from the California Institute of Technology, in 1995 and 1999 respectively. After a postdoctoral position at the Harvard University Physics Department and a faculty position at the University of Washington, she moved to UC Berkeley…

Find out more »## May 2019

### Peter Constantin, Princeton University – Brauer Lecture Day 1

Overall Title: "Fluid nonlinearity" Lecture I: Smooth and dissipative solutions of Euler equations, Navier-Stokes equations and the zero viscosity limit. Abstract: I will describe briefly basic questions of the area. Then I will discuss some of the recent results: 1) smooth multiscale solutions with compactly supported velocity and 2) conditions away from the boundary for the zero viscosity limit to be given by possibly dissipative solutions of Euler equations. Biography: Dr. Peter Constantin, Princeton University, Princeton, NJ. Dr. Peter Constantin holds…

Find out more »### Peter Constantin, Princeton University – Brauer Lecture Day 2

Overall Title: “Fluid nonlinearity” Lecture II: Nernst-Planck-Navier-Stokes Equation Abstract: I will describe recent work concerning this system of equations describing ionic diffusion in fluids in the presence of boundaries with different kinds of properties. Biography: Dr. Peter Constantin, Princeton University, Princeton, NJ. Dr. Peter Constantin holds degrees from the University of Bucharest, where he graduated "summa cum laude" in 1975, and from the Hebrew University of Jerusalem, where he received his PhD in 1981 with Professor Shmuel Agmon as his advisor. From…

Find out more »### Peter Constantin, Princeton University – Brauer Lecture Day 3

Overall Title:“Fluid nonlinearity” Lecture III: SQG in bounded domains. Abstract:I will present a global interior regularity result. Biography: Dr. Peter Constantin, Princeton University, Princeton, NJ. Dr. Peter Constantin holds degrees from the University of Bucharest, where he graduated "summa cum laude" in 1975, and from the Hebrew University of Jerusalem, where he received his PhD in 1981 with Professor Shmuel Agmon as his advisor. From 1985 to 2009 he was a professor at the University of Chicago, before moving to…

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