Boris Feigin教授(Kyoto University / Landau Institute for Theoretical Physics)によるスーパーグローバルコース数学特別講義を下記の要領で行います。
- 科目名
- スーパーグローバルコース数学特別講義4
- 日 時
- 2017年7月10日(月)〜14日(金) いずれも14:45〜17:15
- 場 所
- 京都大学理学部3号館 127大会議室
- 題 目
- W-algebras - introduction, screenings and quantum groups
- 概 要
- 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.
- 言 語
- 英語
- 備 考
- 本講義は録画し、Web上で公開します。講義室前方はカメラに写る場合がありますので、予めご了承下さい。