Friday 11.03.2016

Post date: Apr 05, 2016 12:20:55 PM

This was part I of two lectures on the geometric definition of VOA. We mostly discussed background and motivation

• • Sketched G. Segal's definition of CFT.

  • Introduced the rigged moduli space of which there are two models: (1) Bordered Riemann surfaces where each boundary component is parametrized by S^1. (1) Punctured Riemann surfaces with local coordinate charts specified in a neighborhood of each puncture.

  • In higher-genus the complex structure of these moduli spaces requires serious work in Teichmuller theory which I have been working on for many years. We recently finished a review article: Quasiconformal Teichmuller theory as an analytical foundation for two dimensional conformal field theory

• Stated the "Geometric definition of a VOA". (Which is based on the genus zero rigged moduli space). The sources for this are Yi-Zhi Huang's book and also his article in the Proc. Nat. Acad. Sci. "Geometric interpretation of vertex operator algebras".