# 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".