Speaker : Professor Miranda C.N. Cheng (Institut de Mathematiques de Jussieu)
Title : Umbral Moonshine
Time : 2012-12-20 (Thu) 14:00-15:00
Place : Seminar Room 722, Institute of Mathematics (NTU Campus)
Abstract: Mock modular forms are generalizations of modular forms first introduced by Ramanujan. Their properties had been mysterious for 80 years until various breakthroughs in the past 10 years. In the last century, the Monstrous Moonshine Conjecture initiated the study of the fascinating relation between modular forms and sporadic groups. In this colloquium I will report a conjecture on a new type of "umbral moonshine" relating a set of mock modular forms, including many of Ramanujan's original examples, and the representation theory of a set of finite groups. One instance of such a surprising umbral moonshine phenomenon relates the largest Mathieu group to the geometry of K3 surfaces, as was first observed by Euguchi-Ooguri-Tachikawa in 2010. However, the origin and the explanation of this umbral moonshine is still unknown. This talk is based on the arXiv pre-print: 1201.4140, 1204.2779 with John Duncan and Jeff Harvey.