Modular invariance of characters of a rational conformal field theory has been known since the work of Cardy, and it was proved by Zhu for rational and C_2-cofinite vertex operator algebras (VOA), which constitute a mathematical formalization of RCFT. This talk will discuss the modularity of trace functions in rational orbifold theory. We will also propose how to use the modularity to characterize the rationalilty of vertex operator algebras.

Speaker's Bio: Dong Chongying is a Chair Professor at the University of California, Santa Cruz, a Fellow of the American Mathematical Society, a recipient of the National Outstanding Youth Fund, and a "Changjiang Scholar" Chair Professor. She mainly engages in research on vertex operator algebras and infinite dimensional Lie algebras. He has made significant contributions in the fields of vertex operator algebra, Orbifold theory, and generalized moonlight conjecture. He has published over 120 academic papers in journals such as Acta. Math., Duke. Math. J., Amer. J. Math., Crelle's Journal, Com. Math. Phys., and has been cited more than 7800 times.