# Brauer Lectures

## The UNC Alfred T. Brauer Lectures

Alfred Brauer (1894–1985) had a profound impact on the Mathematics Department at UNC. Born in Germany, he held a position at the University of Berlin until the advent of the Nazis during the 1930s. He fled the country in 1939, accepting Hermann Weyl’s invitation to the Institute for Advanced Study in Princeton. He came to North Carolina in 1942, teaching here until his retirement in 1966. During this time he founded the Mathematics and Physics Library, using his knowledge and expertise to establish a superb collection. In appreciation for this effort the library was named for him in 1976. Alfred Brauer was honored by the University with the award of a Kenan professorship in 1959, the Tanner Award for excellence in undergraduate teaching in 1965, and an honorary doctor of legal letters degree in 1972. He has also received honors from outside the University, including the Oak Ridge Science Award and the G.W.F. Hegel Medal from the University of Berlin. In 1975 an Alfred T. Brauer Instructorship was created at Wake Forest University, where he taught after his retirement from the University of North Carolina. The Alfred Brauer Fund was established by the Department of Mathematics in 1984 on the occasion of his ninetieth birthday.

### 2018 Schedule:

There are no upcoming events at this time.

To honor the memory of Alfred Brauer and to recognize his many contributions to the Mathematics Department at UNC, the Alfred Brauer Lectures were begun in 1985.

The 2018 Brauer Lectures will be given by **Dr. Mina Aganagic **on April 10-12, 2018.

The 2017 Brauer Lectures were given by Mikhail Khovanov, on March 29-31, 2017.

The 2016 Brauer Lectures were given by Stan Osher, on April 20-22, 2016.

The 2015 Brauer Lectures were given by Michael Hopkins, on March 23-25, 2015.

The 2014 Brauer Lectures were given by Simon Donaldson, on March 24-26, 2014.

The 2013 Brauer Lectures were given by Vaughan Jones, University of California at Berkeley and Vanderbilt University, on March 4-6, 2013.

The 2012 Brauer Lectures were given by Alex Lubotzky, Hebrew University, on April 16-18, 2012.

The 2011 Brauer Lectures were given by Gerard Laumon of CNRS and Paris-Sud (Orsay) on March 28-30, 2011.

The 2010 Brauer Lectures were given by Alex Eskin of the University of Chicago.

### 2018 Brauer Lecturer:

**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 in 2004. Early in her career, she was named a Sloan Fellow and a DOE Outstanding Junior Investigator. In 2016 she received a prestigious Simons Foundation Investigator award.

Titles and Abstracts:

**Lecture 1: “Lesson on Integrability”**

Quantum Knizhnik-Zamolodchikov Equation is a difference generalization of the famous Knizhnik-Zamolodcikov equation. The equation itself, its solutions, and its monodromies all turn out to emerge from geometry of a certain class of holomorphic symplectic varieties. This connection between geometry and representation theory can be understood starting from a certain string theory in six dimensions. As an application, from the six dimensional perspective we will discover relations between several different approaches to integrable lattice models, including the one of Nekrasov and Shatshvili, and that of Costello with Witten and Yamazaki. (The lecture is based on joint works with Andrei Okounkov, and work to appear with Nikita Nekrasov and Samson Shatashvili).

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**Lecture 2: “Lesson on Knot Categorification”**

I will describe three paths to categorification of Reshetikhin-Turaev-Witten invariants of knots, and the relations between them. The first approach is based on derived categories of coherent sheaves on intersections of slices in affine Grassmannians. The second is based on Fukaya-Seidel categories of their mirrors. The third approach is based on counting solutions to five dimensional equations with gauge theory origin, due to Witten. All three approaches have a common starting point in the six dimensional string theory. (The lecture is based on joint works to appear, with Andrei Okounkov and with Dimitrii Galakhov.)

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**Lecture 3: “Lesson on Geometric Langlands”**

One manifestation of Langlands duality turns out to be an identification between the q-conformal blocks of the quantum affine algebra and the deformed W-algebra associated to two Langlands dual Lie algebras. The proof of the correspondence (in the simply laced cases) relies on recent results in quantum K-theory of the Nakajima quiver varieties. The “quantum q-Langlands correspondence” is best understood starting with string theory in six dimensions. The six dimensional perspective leads to many extensions of the correspondence, and also explains the relation to the work of Kapustin and Witten. (The lecture is based on joint work with Edward Frenkel and Andrei Okounkov.)

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