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