Fall, 2004

• Speaker L. Kong, Rutgers University
  • Title Conformal field algebras and tensor categories
  • Time/place Friday, 10/1/2004 3:00 pm in Hill 705
  • Abstract Conformal field theories have both holomorphic and antiholomorphic parts, which are sometimes called chiral conformal field theories. In genus-zero and genus-one cases, chiral conformal field theories have been constructed from a general class of vertex operator algebras and their representations, and in general these theories have monodromies. To construct conformal field theories without monodromies, we need to put chiral theories together to cancel the monodromies. In genus-zero, such conformal field theories are described by what we call "conformal field algebras." In this talk, we will discussion the notion of conformal field algebra, their relation with algebras in tensor categories, and a construction of such algebras.

• Speaker P. Etingof, MIT
  • Title Cherednik and Hecke algebras of orbifolds
  • Time/place Friday, 10/15/2004 3:00 pm in Hill 705
  • Note Joint Algebra/Quantum Mathematics Seminar
  • Abstract The rational Cherednik algebra is attached to a finite group G acting on a vector space V, i.e. to the orbifold V/G. I will explain how the theory of Cherednik algebras can be extended to an arbitrary orbifold (algebraic or complex analytic), and how to define the KZ functor for such algebras. This leads to a construction of a flat deformation of the group algebra of the orbifold fundamental group of any complex orbifold Y whose universal cover has a finite second homotopy group. These deformations include all known Hecke algebras (usual, complex reflection, affine, double affine). The talk is based on my paper math.QA/0406499.

• Speaker L. Zhang, Rutgers University and Sequent Capital LLC
  • Title When does the commutator formula imply the Jacobi identity in vertex operator algebra theory?
  • Time/place Friday, 10/22/2004 3:00 pm in Hill 705

• Speaker A. Ocneanu, Pennsylvania State University
  • Title Modular theory, quantum subgroups and quantum field theory
  • Time/place Friday, 10/29/2004 3:00 pm in Hill 705
  • Abstract We describe the connections between modular invariants, topological quantum doubles and the construction and classification of quantum subgroups. We discuss applications to quantum field theoretical models.

• Speaker Keith Hubbard, University of Notre Dame and Rutgers University
  • Title Vertex operator coalgebras: Their operadic motivation and concrete constructions
  • Time/place Friday, 11/5/2004 3:00 pm in Hill 705
  • Abstract Arising from the study of conformal field theory, vertex operator coalgebras model the surface swept out in space-time as a closed string splits into two or more strings. By studying the theory of operads, a structure introduced by May to study iterated loop spaces, the structure of both vertex operator algebras and vertex operator coalgebras may be developed. This talk will define the notion of operad, show how operads geometrically motivate associative algebras and coassociative coalgebras, and then analogously use operads to motivate vertex operator algebras and vertex operator coalgebras. The talk will conclude with examples of vertex operator coalgebras that are constructed via vertex operator algebras with appropriate bilinear forms.

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