Mock modular forms in combinatorics and arithmetic geometry

March 8 to March 12, 2010

at the

American Institute of Mathematics, San Jose, California

organized by

Kathrin Bringmann, Ken Ono, and Sander Zwegers

Original Announcement

This workshop will focus on mock modular forms as they occur in combinatorics and arithmetic geometry and explore some other potential applications.

In recent years there has been a flurry of activity in the area of mock modular forms. Despite the recent rapid development, many open problems and further applications still need to be addressed. The primary goal of this workshop is to focus on some of the different areas of mathematics and physics that could benefit from the many recent advances in the subject.

Below is a partial list of topics to be discussed during the workshop. The participants are more than welcome to suggest related topics of their interest.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

Papers arising from the workshop:

l-adic properties of the partition function
by  Amanda Folsom, Zachary A. Kent, and Ken Ono
The partition function and Hecke operators
by  Ken Ono,  Adv. Math. 228 (2011), no. 1, 527-534  MR2822238
Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms
by  Jan Hendrik Bruinier and Ken Ono,  Adv. Math. 246 (2013), 198-219  MR3091805
CM values of automorphic Green functions on orthogonal groups over totally real fields
by  Jan H. Bruinier and Tonghai Yang
Mock modular forms as p-adic modular forms
by  Kathrin Bringmann, Pavel Guerzhoy, and Ben Kane
Eichler-Shimora theory for mock modular forms
by  Kathrin Bringmann, Pavel Guerzhoy, Zachary Kent, and Ken Ono