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The Erwin Schroedinger Institute for Mathematical Physics

Moonshine

Eguchi, Ooguri and Tachikawa (EOT) initiated a new era in moonshine in 2010, by observing a relationship between representations of the Mathieu group M24 and the elliptic genus of a K3 surface. As it ties in Calabi-Yau geometry and supersymmetric string theory, this Mathieu moonshine observation has generated a lot of interest and activity. By now Mathieu moonshine has been recognized as a special case of umbral moonshine, and several other new instances of moonshine have been discovered in recent years. The relationship between K3 (sigma model) symmetries and M24 has been clarified, but not in a way that resolves the EOT observation. There are many important questions that will take time to solve.

The topic of this workshop is moonshine phenomena, and should be understood in the broadest sense. Current interesting topics that we plan to cover at the workshop are the following:

  • New moonshine phenomena and potential interconnections between them.
  • The search for a unified way of understanding the different moonshine phenomena and ideas towards classifying moonshine phenomena.
  • Enumerative geometry of K3 surfaces and higher dimensional Calabi-Yau manifolds and their potential connection to moonshine.
  • Recent developments in the study of automorphic forms and potential connections to physics.
  • Black hole microstate counting and wall crossing.
  • Recent developments in VOAs and CFTs in two dimensions and their applications to moonshine.
  • The relation between quantum gravity in three dimensions and CFTs in two dimensions.
  • Applications of moonshine to arithmetic geometry.

At a glance

Type: Workshop
When: Sep 10, 2018 to
Sep 14, 2018
Where: ESI, Boltzmann Lecture Hall
Organizers: John Duncan (Emory U, Atlanta), Anne Taormina (Durham U), Katrin Wendland (U of Freiburg), Timm Wrase (TU Vienna)
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