GDO

Abstract

Modular forms occur in many different parts of number theory and other fields of mathematics. In this talk we will discuss two places where generalised modular forms appear in connection with the theory of finite groups. One is the occurrence of "quasimodular forms" in the representation theory of symmetric groups (and in related questions concerning coverings of Riemann surfaces), the other, the fairly recent discovery of an unsuspected connection between the theory of "mock modular forms" and the representation theory of one of the sporadic simple groups.