Spring, 2006

• Speaker Andy Linshaw, Brandeis University
  • Title Chiral equivariant cohomology
  • Time/place Friday, 2/24/2006 1:00 pm in Hill 705
  • Abstract I will discuss a new cohomology theory that extends H. Cartan's cohomology theory of G^* algebras. The latter is an algebraic abstraction of the topological equivariant cohomology theory for G-spaces, where G is a compact Lie group. Cartan's theory, discovered in the 50s and further developed by others in the 90s, gave a de Rham model for the topological equivariant cohomology, the same way ordinary de Rham theory does for singular cohomology in a geometric setting. The chiral equivariant cohomology takes values in a vertex algebra and includes Cartan's cohomology as a subalgebra. I will give a brief introduction to vertex algebras, and then discuss the construction of the new cohomology and some of the basic results and examples. This is a joint work with Bong Lian and Bailin Song.

• Speaker Haisheng Li, Rutgers University at Camden
  • Title A smash product construction of nonlocal vertex algebras
  • Time/place Friday, 2/17/2006 1:00 pm in Hill 705
  • Abstract We first introduce a notion of vertex bialgebra and a notion of module nonlocal vertex algebra for a vertex bialgebra and then we present a smash product construction of nonlocal vertex algebras. For every nonlocal vertex algebra V satisfying a suitable condition, we construct a canonical bialgebra B(V) such that primitive elements of B(V) are essentially pseudo derivations and group-like elements are essentially pseudo endomorphisms. Furthermore, vertex algebras associated with Heisenberg Lie algebras as well as those associated with nondegenerate even lattices are reconstructed through smash products.

• Speaker John Duncan, Yale University
  • Title Vertex operators and sporadic groups
  • Time/place Friday, 1/20/2006 1:00 pm in Hill 705
  • Abstract In the 1980's, Frenkel, Lepowsky and Meurman demonstrated that the vertex operators of mathematical physics play a role in finite group theory by defining the notion of vertex operator algebra, and constructing an example whose full symmetry group is the largest sporadic simple group: the Monster. In this talk we describe an extension of this phenomenon by introducing the notion of enhanced vertex operator algebra, and constructing examples that realize other sporadic simple groups, including ones that are not involved in the Monster.