Mock Modular Forms, Moonshine, and String Theory: August 26 – 30, 2013

Organized by Miranda Cheng, Matthias Gaberdiel, and Terry Gannon.

Dates: August 26 – 30, 2013

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Since 2010, there has been a rapid development in the study of moonshine phenomena relating mock modular forms and finite groups. Following the observation in 2010 on the relation between the elliptic genus of K3 surfaces and the largest Mathieu sporadic group M24, a relation between M24 and a mock theta function has been largely established after a collective effort by various researchers. Moreover, a family of examples of moonshine involving mock modular forms, extending the M24 relation, has been proposed and dubbed “Umbral Moonshine”. However, in either case the origin of such a mysterious relation remains unknown. In particular, the possible relation to K3 geometry and to string and conformal field theory is tantalising but poorly understood at the moment. Clearly, a lot of treasure remains to be uncovered in the future study of this new moonshine phenomenon, and the time seems ripe for significant progress towards identifying the underlying source of Mathieu and Umbral Moonshine. This workshop, situated at the crossroads of physics and mathematics, will bring together researchers in string theory, vertex operator algebras, generalised Kac-Moody algebras, number theory, and algebraic geometry.

Since 2010, there has been a rapid development in the study of moonshine phenomena relating mock modular forms and finite groups. Following the observation in 2010 on the relation between the elliptic genus of K3 surfaces and the largest Mathieu sporadic group M24, a relation between M24 and a mock theta function has been largely established after a collective effort by various researchers. Moreover, a family of examples of moonshine involving mock modular forms, extending the M24 relation, has been proposed and dubbed “Umbral Moonshine”. However, in either case the origin of such a mysterious relation remains unknown. In particular, the possible relation to K3 geometry and to string and conformal field theory is tantalising but poorly understood at the moment. Clearly, a lot of treasure remains to be uncovered in the future study of this new moonshine phenomenon, and the time seems ripe for significant progress towards identifying the underlying source of Mathieu and Umbral Moonshine. This workshop, situated at the crossroads of physics and mathematics, will bring together researchers in string theory, vertex operator algebras, generalised Kac-Moody algebras, number theory, and algebraic geometry.

This workshop is a part of the Fall 2013 program, Mock Modular Forms, Moonshine, and String Theory, which is organized by Miranda Cheng, Matthias Gaberdiel, and Terry Gannon. This program takes place from August 26 – September 27, 2013.

*All talks will be held in the Lecture Hall (Room 102)