This is the website for the reading seminar on vertex algebras and vertex operator algebras running at the University of Edinburgh School of Mathematics in Semester 2 of 2020-2021.
The seminar meets on Zoom at 5pm on Wednesdays, starting Wednesday 20 January. Contact Sue Sierra for the Zoom details.
Tentative schedule of talks and topics
This is a tentative outline of the seminar, which will certainly change as the semester goes on.
Vertex algebra basics: definition, relation to other algebraic structures (Sue Sierra) slides video
Representation theory of affine Kac-Moody algebras (including fusion product and some discussion of the Kazhdan-Lusztig equivalence) (Ben Davison) slides video
Examples I: Affine Kac-Moody vertex algebras, the Virasoro vertex algebra (Brian Williams) slides video
Vertex Lie algebras and classical limits (Johan Martens) slides video
C_2 algebras a la Zhu, associated varieties (Jenny Brown) slides video
Rational conformal field theory and modular tensor categories (Patrick Kinnear) slides video
The Costello-Gwilliam approach (Brian Williams) slides video
The chiral de Rham complex and chiral differential operators (Brian Williams) slides video
References
Our main reference for the seminar will be the book Vertex Algebras and Algebraic Curves (2nd edition), by Frenkel and Ben-Zvi. Contact Sue Sierra for access to the book.
Other references include:
Arakawa and Moreau's notes on W-algebras
Dietrich Burde's notes on pre-Lie algebras, which discuss their connection with vertex algebras briefly.
In addition, Anne Moreau's web page has a useful bibliography on W-algebras