Michael Mertens: Class Numbers, Finite Simple Groups, and Arithmetic

Abstract: In recent years, the subject of Moonshine, which provides a still somewhat surprising connection between the theory of modular forms and the representation theory of finite groups — most notably the Monster group, has also been connected to arithmetic questions. In my talk I’m going to discuss some first steps in order to investigate such connections systematically. In particular, I am going to present some new versions of moonshine for several of the sporadic simple Mathieu groups, as well as an infinite family of finite simple groups as well as arithmetic connections, e.g., for the famous Congruent Number Problem.

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