Fall, 2003

• Speaker Liang Kong, Rutgers University
  • Title Open-string vertex algebras (jointly with Y.-Z. Huang)
  • Time/place Friday, 10/3/2003 3:00 pm in Hill 425
  • Abstract We introduce notions of open-string vertex algebra, conformal open-string vertex algebra and variants of these notions. These are "open-string-theoretic," "noncommutative" generalizations of the notions of vertex algebra and of conformal vertex algebra. Given an open-string vertex algebra, we show that there exists a vertex algebra, which we call the "meromorphic center" inside the original algebra such that the original algebra yields a module and also an intertwining operator for the meromorphic center. This result gives us a general method for constructing open-string vertex algebras. Besides obvious examples obtained from associative algebras and vertex (super)algebras, we give a nontrivial example constructed from the minimal model of central charge c = 1/2 . We also discuss the relationship between the gradingrestricted conformal open-string vertex algebras and the associative algebras in braided tensor categories. We also discuss a geometric and operadic formulation of the notion of such algebra and the relationship between such algebras and a so-called "Swiss-cheese partial operad."

• Speaker Benjamin Doyon, Rutgers University, Physics Department
  • Title From vertex operator algebras to the Bernoulli numbers
  • Time/place Friday, 10/31/2003 3:00 pm in Hill 425
  • Abstract

• Speaker Geoff Buhl, Rutgers University
  • Title Complete reducibility and C_n-cofiniteness of vertex operator algebras
  • Time/place Friday, 11/7/2003 3:00 pm in Hill 425
  • Abstract

• Speaker Lin Zhang, Rutgers University
  • Title A vertex operator algebra approach to the construction of a tensor category of Kazhdan-Lusztig
  • Time/place Friday, 11/21/2003 3:00 pm in Hill 425
  • Abstract In contrast to the ordinary tensor product of modules for a Lie algebra, the known construction of the tensor product of modules of a fixed level for an affine Lie algebra is completely nontrivial and in essence uses ideas from conformal field theory. As a payoff it produces a braided tensor category structure. I will first summarize Kazhdan-Lusztig's construction of this tensor product, and then, using recent joint work with Huang and Lepowsky, I will show how this can be incorporated into vertex operator algebra theory and how the braided tensor category can be proved to in fact have a "vertex tensor category" structure. I will also present another application of this work that is related to the module category for vertex algebras associated with hyperbolic even lattices.

• Speaker Victor Ostrik, Institute for Advanced Study
  • Title Finite extensions of vertex algebras
  • Time/place Friday, 12/5/2003 3:00 pm in Hill 425
  • Abstract In this talk we will discuss the problem of classification of all extensions V\subset V' of a given vertex algebra V such that V' is a finite length module over V. Under certain assumptions on the algebra V this problem is equivalent to the classification of commutative algebras in the tensor category of V-modules (Huang-Kirillov-Lepowsky). We review what is known about the latter problem, in particular known classification results for affine Lie algebras on positive integer level and for holomorphic orbifolds.

• Speaker Matthew Szczesny, University of Pennsylvania
  • Title Orbifolding the chiral de Rham complex
  • Time/place Friday, 12/12/2003 3:00 pm in Hill 425
  • Abstract Given a smooth variety X with the action of a finite group G, we construct twisted sectors for the chiral de Rham complex from sheaves of twisted modules supported along fixed point sets. The BRST cohomology of the twisted sectors is isomorphic to the Chen-Ruan orbifold cohomology of the orbifold [X/G], and the partition function yields the orbifold elliptic genus.