290C Conformal Field Theory

Spring 2016

This seminar will discuss the vertex operator algebras approach to conformal field theory.

Topics:

Classical definition of vertex algebras, locality, reconstruction
Virasoro, Heisenberg
Lattice vertex algebras, affine algebras
Modules over vertex algebras, rational vertex algebras
Modularity
Monster voa, Moonshine
Chiral algebras, Ran spaces, factorization algebras
Operadic definition

Wednesday March 30, 2pm, MS 6118 Introduction (R.Rouquier)
Wednesday April 13, 11am-1pm (MS6905) Vertex algebras: definition and Heisenberg (Jeremy Brightbill)
Wednesday April 20, 11am-1pm (MS6905) Lattice vertex algebras and affine algebras (Dustan Levenstein)
Wednesday May 4, 11am-1pm (MS6905) Operadic approach to vertex algebras (Ben West)
Wednesday May 11, 11am-1pm (MS6905) Factorization algebras (Pax Kivimae)
Wednesday May 18, 11am-1pm (MS6905) Conformal blocks (William Schlieper)
Wednesday May 25, 11am-1pm (MS6905) Modularity of representations of rational voas (Kevin Carlson)


References:

Ben-Zvi and Frenkel, Vertex algebras and algebraic curves
Kac, Vertex algebras for beginners
Kac, Notes on vertex algebras
Beilinson and Drinfeld, Chiral Algebras
Beilinson: course on chiral algebras  Part 1 35pp. and Part 2 21pp. (MIT, Fall 1995)
Francis and Gaitsgory, Chiral Koszul duality
Raskin, Chiral categories
Huang, Two-dimensional conformal geometry and vertex operator algebras
Frenkel, Lepowsky and Meurman, Vertex operator algebras and the Monster