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

Attendee List

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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)

Mock Modular Forms, Moonshine, and String Theory Workshop Schedule

Time Title Presenters  Video
 9:00am Regisration/Breakfast Simons Center Cafe
10:00am Moonshine – an overview Terry Gannon video
11:00am Mathieu Moonshine – an overview Matthias Gaberdiel video
12:00pm Lunch Simons Center Cafe
 1:30pm Special numbers and functions related to mock modular forms Ken Ono video
slides
 2:30pm The Mathieu group and automorphisms of K3 Dave Morrison video
 3:30pm Tea Time Simons Center 1st Floor Outside Patio


Time Title Presenters  Video
 9:00am Breakfast Simons Center Cafe
10:00am
Umbral Moonshine — An Overview of Mock Moonshine Beyond M24
Miranda Cheng video
11:00am Locally harmonic weak Maass forms Kathrin Bringmann video
12:00pm Lunch Simons Center Cafe
 1:30pm Generalised Mathieu Moonshine Roberto Volpato video
slides
 2:30pm Monstrous Lie algebras Scott Carnahan video
 3:30pm Tea Time Simons Center 1st Floor Outside Patio

Time Title Presenters  Video
 9:00am Breakfast Simons Center Cafe
10:00am Moonshine and N=2/4 superconformal algebra Kazuhiro Hikami video
11:00am Mathieu Moonshine, Calabi-Yau compactifications, and (0,4) superconformal theories Shamit Kachru video
12:00pm Lunch Simons Center Cafe
 1:30pm Moonshine in Fivebrane Spacetimes Jeff Harvey video
 2:30pm Multiplicative Moonshine Geoffrey Mason video
slides
 3:30pm Tea Time Simons Center 1st Floor Outside Patio
 6:00pm Workshop Dinner Banquet Simons Center Cafe

Time Title Presenters  Video
 9:00am Breakfast Simons Center Cafe
10:00am Mathieu Moonshine and the Geometry of K3 Surfaces Thomas Creutzig video
11:00am Symmetry-surfing the moduli space of Kummer K3s Anne Taormina video
12:00pm Lunch Simons Center Cafe
 2:30pm Majorana Representations, the Monster and the Straight Flush Conjecture-abstract Alexander Ivanov video
 3:30pm Tea Time Simons Center 1st Floor Outside Patio
 4:00pm Colloquium Talk- K3 surface and moonshine phenomenon Tohru Eguchi video


Time Title Presenters  Video
 9:00am Breakfast Simons Center Cafe
10:00am Recent results about the Monster, vertex algebras and modular moonshine Robert L. Griess, Jr. video
slides
11:00am Moonshine for M12 Suresh Govindarajan video
12:00pm Lunch Simons Center Cafe
 3:30pm Tea Time Simons Center 1st Floor Outside Patio

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