Fall 2016

Dec. 8, 2016

Speaker: Johannes Flake

Title: Examples of VOAs and their modules II

Abstract: [Second part of last weeks' talk.] I will present the construction of VOAs and their modules following chapter 6 of Lepowsky/Li. Presumably, the constructions associated to the Virasoro algebra and to affine Lie algebras will exhaust our time. If not, we could look at the case of Heisenberg algebras, as well.

Dec. 1, 2016

Speaker: Johannes Flake

Title: Examples of VOAs and their modules I

Abstract: I will present the construction of VOAs and their modules following chapter 6 of Lepowsky/Li. Presumably, the constructions associated to the Virasoro algebra and to affine Lie algebras will exhaust our time. If not, we could look at the case of Heisenberg algebras, as well.

Nov. 17, 2016

Speaker: Fei Qi

Title: Rationality of products and iterates for more than 3 vertex operators

Abstract: We know very well that the product and the iterate of two vertex operators makes sense in terms of formal variable. However what's the story for the product and iterate of more than three vertex operators? It turns out that for vertex algebras this is not a problem, yet for MOSVAs this is a problem. We shall see why.

Nov. 10, 2016

Speaker: Jongwon Kim

Title: Representation Theory of Vertex Algebras II

Abstract: Last time, we showed the equivalence of a V-module structure on W and a representation of V on W in the setting of its canonical weak vertex algebra E(W). We will determine when a subalgebra of E(W) is indeed a vertex algebra or a vertex operator subalgebra. Then we will go over some construction theorems for vertex algebras and modules in a similar spirit.

Nov. 3, 2016

Speaker: Terence Coelho

Title: Representation Theory of Vertex Algebras I

Abstract: I will introduce the notion of a representation of a Vertex Algebra and introduce the machinery that will be used to show the equivalence of a V-module structure on W (where V is a vertex algebra and W a Vector Space) with a representation of V on W.

Oct. 20, 2016

Speaker: Vernon Chan

Title: Commutativity, Associativity and Skew-Symmetry of Vertex Algebras and Modules II

Abstract: [Second part of last week's talk.] Basic properties of vertex algebras, including different forms of commutativity, associativity, and skew-symmetry, will be discussed. I will show that some combinations of these properties are equivalent to the Jacobi identity of the vertex algebra, and whenever possible, generalize them to the setting of module actions of a vertex algebra. They will be important tools for proving something is a module.

Oct. 13, 2016

Speaker: Vernon Chan

Title: Commutativity, Associativity and Skew-Symmetry of Vertex Algebras and Modules

Abstract: Basic properties of vertex algebras, including different forms of commutativity, associativity, and skew-symmetry, will be discussed. I will show that some combinations of these properties are equivalent to the Jacobi identity of the vertex algebra, and whenever possible, generalize them to the setting of module actions of a vertex algebra. They will be important tools for proving something is a module.

Spring 2013, Fall 2012 (Organized by Shashank Kanade)