Umbral Moonshine
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Thu, 08/03/2012 15:00 |
John Duncan |
Representation Theory Seminar  |
L3 |
| In April 2010 Eguchi–Ooguri–Tachikawa observed a fascinating connection between the elliptic genus of a K3 surface and the largest Mathieu group. We will report on joint work with Miranda Cheng and Jeff Harvey that identifies this connection as one component of a system of surprising relationships between a family of finite groups, their representation theory, and automorphic forms of various kinds Mock modular forms, and particularly their shadows, play a key role in the analysis, and we find several of Ramanujan's mock theta functions appearing as McKay–Thompson series arising from the umbral groups. | |||