Matthew Szczesny (UPenn Philadelphia):
The chiral de Rham complex, orbifolds, and
discrete torsion
The chiral de Rham complex is a sheaf of vertex algebras
associated to every smooth complex variety X, introduced by Malikov,
Schechtman, and Vaintrob in 1999. Its cohomology is believed to be related
to the sigma-model with target X. We describe joint work with Edward
Frenkel, as well as Lev Borisov and Anatoly Libgober on constructing the
chiral de Rham complex of an orbifold and introducing discrete torsion. We
show how orbifold elliptic genera and orbifold cohomology appear in the
picture. We also show that the elliptic genus with discrete torsion
associated to a Calabi-Yau orbifold is a Jacobi form, and prove a formula
for the generating function of genera of symmetric products (with torsion)
originally obtained by Dijkgraaf.