Vertex operator algebras
Evgeny Feigin
Skoltech, spring 2020
News
The exam problems are now availbale. Please return the solutions no later than Thursday, May 28, 2pm.
Lectures
03.02. Semi-infinite wedge space, charge and energy decomposition, Heisenberg operators.
10.02. Boson-fermion correspondence, wedging and contracting operators, vetex operatots.
17.02. Operator valued series, fields, conformal dimension, delta function, locality.
02.03. Correlation functions and locality. Definition of vertex operator algebras. Commutative VOAs. Heisenberg VOA.
16.03. Normal ordering, Dong's Lemma, Reconstruction theorem (weak version).
30.03. Kac-Moody VOA and Virasoro VOA. Conformal structures on vertex operator algebras.
06.04. The Goddard uniqueness theorem, skew-symmetry and associativity.
13.04. The proof of the associativity theorem. Operator product expansion (OPE). Normally ordered products.
27.04. Commutation relations and singular part of the OPE. Conformal structures. Strong reconstruction theorem.
04.05. Tensor products of VOAs, VOA structure on the Laurent polynomials algebra. Commutation relations between Fourier coefficients and bilinear operation on V[t,t^{-1}].
11.05. Representations of vertex operator algebras, compatibility with translation operator and mutual locality. Smooth and coherent modules of the Lie algebra U'(V).
18.05. Equivalence between the categories of VOA modules and coherent U'(V) modules.. Fock modules and 1d lattices.
08.06. Globalizing vertex operator a;gebras: automorphisms, coordinates on a disk, torsors and twists
Results
results (last update 20.05)
Books
V. Kac, A. Raina, N.Rozhkovskaya, Bombay lectures on. Highest-weight representations of infinite-dimensional Lie algebras.
V.Kac, Vertex algebras for beginners.
E.Frenkel, D.Ben Zvi, Vertex algebras and algebraic curves.