Seminar series
Date
Mon, 21 Jan 2013
Time
12:00 -
13:00
Location
L3
Speaker
Miranda Cheng
Organisation
Jussieu
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 talk 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 elliptic genus of K3 surfaces, as was first observed by Euguchi-Ooguri-Tachikawa in 2010. Moreover, there are hints suggesting that all occurrences of umbral moonshine have a close relation to K3-compactifications of string theory. However, despite of these tantalising hints the origin and the explanation of this umbral moonshine is still unclear at the moment. This talk is based on the arXiv pre-print: 1201.4140, 1204.2779 with John Duncan and Jeff Harvey.