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

Steven Flores gave a series of two lectures. He presented reconstruction theorems and used this approach to construct nontrivial example of vertex (operator) algebras. Detailed typed notes are in the "resources" section 
We continued with algebraic basics following Lepowsky and Li (pages 57  70, 84). In particular we discussed

Following closely the presentation in Lepowsky and Li (see the resources page) we discussed the basics of the calculus of formal power series, the definition of a vertex alegbra and made some informal remarks about the axioms. This material is in chapter 2 and and the first 5 pages of chapter 3. Suggested reading is everything up to and including page 53. Working with formal series has its subtleties, especially the binomial expansion convention. Fill in the details of some proofs to get a feel for it. Another thing is to fill in some details of understanding the 3 variable delta function identities in terms of contour integration. More details appear in the appendix of FrenkelLeposwkyMeurman. If somebody wants to present that it would be great. Let me know if interested. I also suggest you read the introductions to all 4 books listed on the resources page. Next week I plan to discuss (1) some of the axioms which are equivalent to the Jacobi identity (such as weak commutative and the Dderivative property), (2) the definition of vertex operator algebra, and (3) begin discussing the geometric notion of a VOA if time permits. 