### Graduate Student Seminar, 4:00pm January 20, 2003, Hayes-Healy
231

#### Speaker:

#### Title:

Operads: The Geometric Road to Vertex Operator Algebras
#### Abstract:

Operads, or "systems with compositions", were first formally defined in the
1970's by topologists to unify such problems as looking at iterated loop
spaces, compositions of maps and commutativity in simplicial chain complexes
[1]. By taking the geometric structure of a particular operad, one can induce
classical algebraic structures such as monoids, (associative) algebras,
coalgebras and Lie algebras. One can also induce the structure of a vertex
operator algebra (VOA)[2 & 3], which is a non-associative algebra first used
to describe the largest order sporadic finite simple group (the Monster) and
also found to have applications in Conformal Field Theory. We will first
discuss what these operads are as well as examples of them and how they can be
used to induce classical algebraic structures, then look at the operad that
induces the VOA structures along with the basic parts of that structure.
[1] J. Peter May's ``The geometry of iterated loop spaces", Lecture
Notes in Math., No. 271, Springer-Verlag, Berlin, 1972.

[2] Y.-Z. Huang and J. Lepowsky, ``Vertex operator algebras and operads", The
Gelfand Mathematical Seminar, 1990--1992, ed. L. Corwin, I. Gelfand and J.
Lepowsky, Birkhauser, Boston, 1993, 145--161.

[3] Y.-Z. Huang and J. Lepowsky, ``Operadic formulation of the notion of
vertex operator algebra", Mathematical Aspects of Conformal and Topological
Field Theories and Quantum Groups, ed. P. Sally, M. Flato, J. Lepowsky, N.
Reshetikhin and G. Zuckerman, Contemp. Math. 175, Amer. Math. Soc.,
Providence, 1994, 131--148.

To volunteer to give a talk, or for any other questions regarding this schedule, contact Wesley Calvert