Spring, 2007

Spring, 2007

  • Speaker Minxian Zhu, Yale University
    • Title Vertex operator algebras associated to modified regular representations of affine Lie algebras
    • Time/place Tuesday, 1/23/2007 3:30 pm in Hill 425
    • Note Joint Quantum Mathematics/Topology-Geometry Seminar
    • Abstract Vertex operator algebras can be regarded as generalizations of associative algebras, but have much richer structures. We study a family of vertex operator algebras which admit two copies of the affine Lie algebra actions with dual central charges, and whose top levels are identified with regular functions on the Lie groups. We discuss two constructions: one is based on the properties of intertwining operators and Knizhnik-Zamolodchikov equations; the other is to use the enveloping algebra of the vertex algebroid associated to the Lie group and a fixed level. We show that the two constructions yield the same vertex operator algebra. The case of integral central charges will also be discussed.

  • Speaker Bill Cook, Rutgers University
    • Title Vertex operator algebras and recurrence relations
    • Time/place Friday, 3/30/2007 1:00 pm in Hill 705
    • Abstract There are many important classes of examples of vertex operator algebras including Heisenberg VOAs, Virasoro VOAs, lattice VOAs, and the VOAs associated with affine Lie algebras. We will begin with an introduction to the class of VOAs (along with their modules) associated with affine Lie algebras. Then in the latter part of the talk we will discuss an interesting theorem of Haisheng Li. Applying this theorem to our class of examples, we will obtain recurrence relations among the characters of these Vertex Operator Algebras (and VOA modules).

  • Speaker Antun Milas, University at Albany, SUNY
    • Title On a certain family of W-algebras
    • Time/place Friday, 4/6/2007 1:00 pm in Hill 705
    • Abstract Rational conformal field theories can be characterized by the property that there are, up to equivalence, finitely many irreducible representations of the vertex operator algebra, and that every representation is completely reducible. It is tempting to relax the semisimplicity condition and study more general classes of conformal field theories. One such class are rational logarithmic conformal field theories, where not all modules are completely reducible and not even L(0) diagonalizable (here L(0) is the degree zero Virasoro generator). The only known examples of rational LCFT come from certain W-algebras. In this talk, I will first define several families of W vertex algebras. We will then focus on their representations, graded dimensions and various modularity issues. Some parts of the talk are based on a joint work with D. Adamovic.

  • Speaker Vincent Graziano, SUNY at Stony Brook
    • Title G-equvariant modular categories and Verlinde formula
    • Time/place Friday, 4/13/2007 1:00 pm in Hill 705
    • Abstract Many features of a conformal field theory can be captured in the language of categories. Modular tensor categories provide the appropriate framework and we will start by discussing the properites of such a category. We will then introduce the Verlinde algebra associated to such a category, the action of the S-matrix, and the Verlinde formula. Our goal will be to generalize this setup to the case of theories with additional symmetries, such as a vertex operator algebra with a finite group of symmetries. We discuss the extended Verlinde algebra, the S-matrix, and the 'extended' Verlinde formulas.

  • Speaker Corina Calinescu, Ohio State University
    • Title Vertex-algebraic structure of certain modules for affine Lie algebras underlying recursions
    • Time/place Friday, 4/20/2007 1:00 pm in Hill 705
    • Abstract Many combinatorial identities and recursions have been proved or conjectured via vertex operator constructions of representations of affine Lie algebras. In this talk we discuss vertex-algebraic structure of the principal subspaces of all the standard A_1^(1)-modules and we prove suitable presentations for these subspaces. These presentations were used by Capparelli, Lepowsky and Milas for the purpose of obtaining the classical Rogers-Ramanujan and Rogers-Selberg recursions. This is joint work with Jim Lepowsky and Antun Milas.

  • Speaker Tom Robinson, Rutgers University
    • Title A Formal Variable Approach to Special Hyperbinomial Sequences
    • Time/place Friday, 4/27/2007 1:00 pm in Hill 705
    • AbstractIn a nearly self-contained and elementary treatment, we develop the formal calculus used in the theory of vertex algebras to describe certain formal changes of variable. In particular, we extend the logarithmic formal Taylor theorem as found in the work of Y.Z. Huang, J. Lepowsky, and L. Zhang. We apply our results to obtain combinatorial identities concerning generalizations of the Stirling numbers and find that our development leads naturally to a combinatorial definition of the exponential Riordan group which was studied by L.W. Shapiro, S. Getu, W.J. Woan, and L.C. Woodson.