NORTHEASTERN UNIVERSITY
MATHEMATICS DEPARTMENT

REPRESENTATION THEORY AND RELATED TOPICS SEMINAR



Jethro van Ekeren

(MIT)


  Vertex Algebras and Modular Forms

ABSTRACT: Modular forms crop up unexpectedly in several places in representation theory. One very well known example, called monstrous moonshine, is the appearance of coefficients of the J function as dimensions of irreducible representations of the monster group. Another is the modular invariance of graded dimensions of certain modules over an affine Kac-Moody algebra.

These examples find a common generalisation in the theory of vertex algebras, specifically in a theorem of Zhu which implies that the graded dimensions of irreducible modules over a fixed vertex algebra (subject to certain technical requirements) span a finite dimensional space of functions invariant under the modular group. Zhu's proof is intriguing because it is very different than the original proofs of either of the special cases mentioned above, and it uses ideas from geometry and theoretical physics.

In this (purely expository) talk I will introduce the notion of a vertex algebra, explain the statement of Zhu's theorem, outline its proof, and try to motivate the ideas underlying the proof.

January 27, 2012
9:45 - 10:45
(Notice unusual time)
511 Lake Hall


For further information visit http://www.northeastern.edu/martsinkovsky/p/rtrt.html  or contact Alex Martsinkovsky alexmart >at< neu >dot< edu