Top Global Course Special Lectures by Prof. Boris Feigin (Kyoto University / Landau Institute for Theoretical Physics) will take place as follows:
- Course Title
- Top Global Course Special Lectures 4
- Date & Time
- 14:45-17:15 on Monday, July 10 to Friday, July 14, 2017
- Venue
- 127 Conference room, Faculty of Science Bldg. #3, Kyoto University
- Title
- W-algebras - introduction, screenings and quantum groups
- Abstract
- Sometimes people use the words vertex operator algebra and W-algebra as synonyms. This is partly correct, but not entirely. Theory of W-algebras is a collection of extremely interesting examples of new algebraic objects and theory of vertex algebra is an attempt to understand and find some order in this zoo.
- Our lectures are the introduction - so we concentrate on examples and simplest methods of constructing the W-algebras. Note that W-algebras are deeply connected with 2-dimensional conformal field theory. So it is not possible to talk about W-algebras and do not mention some facts from the algebraic geometry of the curves.
- This short course consists of an introduction to random dynamical systems, from a predominantly geometric point of view. The aim is to introduce basic concepts in the context of simple examples. We will discuss some elementary results and highlight open questions.
-
- 1. Clifford algebra, Lattice vertex operator algebras.
- 2. Coinvariants and vertex operators.
- 3. Subalgebras in lattice vertex algebras. Screenings. Quantum groups and screenings.
- 4. Fermionic screenings. Algebra $\widehat{\mathfrak{sl}}(2)$ on a critical level.
- 5. Deformation of universal enveloping of the Lie algebra of differential operators on the circle.
- 6. Plane partitions and W-algebras. (something about recent progress)
- No particular knowledge on representation theory is required.
- Language
- English
- Note
- This series of lectures will be video-recorded and made available online.
Please note that anyone in the front rows of the room can be captured by a video camera.