Courses
Vertex algebras, semi-infinite forms and the boson-fermion correspondence
Speaker: Jethro Van Ekeren (IMPA)Date: Monday, 27 January 2025 - 10:00-12:00Place: Aula Naranja, ICMAT
Abstract:
We will begin with an introduction to vertex algebras, using the language of formal distributions, quantum fields and OPEs, covering basic examples such as the Heisenberg, Virasoro and affine vertex algebras, the b-c and beta-gamma systems, and relations between these classes of examples. We then examine the b-c system (also known as charged free fermions vertex algebra) in more detail, seeing it as the simplest example of a lattice vertex algebra. From this dual picture spring a number of interesting applications : to Schur polynomials in combinatorics, and the KP hierarchy in integrable systems. Further topics might include the Tate central extension and Japanese cocycle, the semi-infinite realisation of the Virasoro algebra and the origin of its critical central charge c = -26, and a proof using vertex algebras of the Kac determinant formula.
Schedule:
22nd January: 10-12
24th January: 10-12
27th January: 10 -12
31st January: 10-12
5th Feb: 10-12
7th Feb: 10-12
