Special Colloquium
Iana I. Anguelova
Centre de Recherches Mathematiques (CRM), Concordia University
Vertex Algebras: From Super to Quantum
Abstract: Vertex operators have been used since the early days of string theory and today they are manifest in diverse areas of mathematics and
physics, ranging from quantum field theory, soliton theory to
representation theory and symmetric functions. Vertex
algebras (which are more or less "singular", "commutative" algebras of
vertex operators) have been introduced to axiomatize the properties of vertex operators. Similarly, the quest is on for a correct definition of a quantum vertex algebra, which should be such
that it accommodates all the existing examples of quantum vertex
operators and their properties. In this talk
I will give a motivation for and explain our definition of an
$H_D$-quantum vertex algebra, where $H_D=C[D]$ is the Hopf algebra of
"infinitesimal translations" generated by D (joint work with Maarten Bergvelt, UIUC). The $H_D$-quantum vertex algebras are a formal parameter quantization, generalizing the Etingof-Kazhdan theory of quantum vertex algebras in various ways. I will show how the bicharacter construction of
vertex algebras (introduced by Borcherds) can be used to handle examples, such as the free fermions. I will briefly mention how this can be applied to the study of fields on anyonic Fock spaces. In conclusion, the outlook towards H-quantum vertex algebras, where H is any Hopf algebra, will be discussed.
There will be a meet and greet right after the talk in SEO 300. Coffee, tea, & cookies will be provided.
Tuesday January 15, 2008 at 3:00 PM in SEO 636