Probability Seminar - Conformal blocks for the Virasoro algebra and tensor categories
报告人：Shinji Koshida (Aalto University)
时间：2025-11-24 14:00-15:00
地点：智华楼-四元厅
Abstract: Conformal field theory in two dimensions can be approached in many ways, but most of them lead to the notion of conformal blocks. These can be viewed either as fundamental objects from which correlation functions are assembled or as "Fourier" kernels governing their decomposition. This talk aims to motivate the study of conformal blocks from the perspective of tensor categories.
The theory of tensor categories of modules for vertex operator algebras has been developed in a substantial body of work by Huang--Lepowsky and Huang--Lepowsky--Zhang. While it is reasonable to treat this machinery as a "black box", I will try to unpack some of its central ideas and highlight how they connect to familiar mathematical constructions.
Liouville CFT presents particular challenges in this context. I will describe a general framework broad enough to include Liouville CFT, with the hope of clarifying how results from probabilistic techniques can be incorporated and what remains to be established.
Bio: I received my PhD in 2018 from The University of Tokyo. I am currently an Academy Research Fellow at Aalto University working on conformal field theory in two dimensions from the algebraic point of view.
