String Theory and the Moonshine Programme
Seminar Room 1, Newton Institute
In some occasions, certain finite groups display a close connection to certain modular objects defined on the upper-half plane. The most well-known of such a relation between these two distinct mathematical structures is the so-called monstrous moonshine, relating the largest sporadic group to a set of modular functions. String theory, with its power to geometrise automorphic objects, has been proven instrumental in providing insights into these mysterious relations. Recently, certain unexpected relation with various similarities to the monstrous moonshine has been discovered. In this talk I will review these recent mathematical developments, while putting extra focus on the role played by string theory.