Michael Mertens

Finite groups and arithmetic

In this talk, we will illustrate some connections between the representation theory of finite groups and the arithmetic of certain modular abelian varieties, in particular elliptic curves. In particular, we will discuss the relatively recent O'Nan Moonshine and its implications regarding class groups and Tate-Shafarevich groups of certain elliptic curves (joint work with J. Duncan and K. Ono), as well as some joint work in progress with M. Cheng and J. Duncan concerning the group 2.M12 (and others).