Introdução à Álgebra de Vértices

After
a brief introduction to Affine Kac-Moody Lie algebras and algebras of vector fields and extensions (Virasoro, Neveu-Schwarz, etc), we will go to the basic structure and representation theory of vertex algebras.

Topics will start with: Calculus with formal distributions, normally ordered products, state-field correspondence. Then we will move to examples: algebras of free Bosons and Fermions, Affine algebras and level, Virasoro algebra and central charge. Supersymmetric extensions of Virasoro. After this we will move to more advanced topics: Boson-Fermion correspondence, lattice vertex algebras and their representations. Homology and W-algebras. Zhu algebras and modularity.

Referências:
K. VICTOR G. – Vertex algebras for Beginners, Volume 10 of University Lecture series of the AMS.
We will also follow Victor G. Kac lecture notes available at: https://impa.br/~heluani/files/lect.pdf.

* Ementa básica. O professor tem autonomia para efetuar qualquer alteração.