Chiral Algebras for the 21st Century

April 15-19, 2019 at UC Davis

This one-week school is aimed at graduate students from both mathematics and physics backgrounds.

It will introduce 2-dimensional chiral algebras (a.k.a. VOA's) from first principles, in a mathematically precise but physically meaningful context, and discuss some of the most exciting applications to current research in physical mathematics. See below for further details.

The school will be led by expert mentors Christopher Beem (Oxford), Thomas Creutzig (Alberta), and Pavel Putrov (ICTP).

For any questions, please contact the organizers, Tudor Dimofte (QMAP) or Philsang Yoo (QMAP & Yale).

A related, more advanced program on QFT for Mathematicians will be taking place at the Perimeter Institute in June 2019.

To apply, fill out the Application Form. Deadline: January 31, 2019

Due to limited space, attendance is by admission only. Students with a math background are expected to have a working knowledge of graduate-level algebra; students with a physics background are expected to be familiar with quantum field theory. Preference will be given to graduate students (though postdocs and faculty are also welcome to apply!).

For graduate students, there will be support for local accommodation.

In more detail, some classic background to be covered in the first part of the week includes

  • Basic examples of rational & irrational VOA's
  • Operations on VOA's: Drinfeld-Sokolov and BRST reduction, cosets, free-field realizations
  • Representation categories and conformal blocks

We will touch upon several modern concepts and developments

  • VOA's as factorization algebras (the modern perspective)
  • Cohomological VOA's, a.k.a. dg chiral algebras
  • Associated varieties

The school will then discuss three central, interrelated research topics:

  • Chiral algebras of Class S
  • Chiral algebras in 4d N=4 super-Yang-Mills, and relation to Geometric Langlands
  • Chiral algebras VOA[M4] associated to 4-manifolds

Lectures will be supplemented by problem sessions.

Lectures will also be recorded, and available online. This school is supported through NSF CAREER grant DMS-1753077.