Conference on "100 Years of Mock Theta Functions; New Directions in Partitions, Modular Forms, and Mock Modular Forms"

Vanderbilt University, Nashville TN

Investigators

Abstract

This award provides partial support for the conference "100 Years of Mock Theta Functions: New Directions in Partitions, Modular Forms, and Mock Modular Forms." This conference falls on the 100 year anniversary of Ramanujan's original definition in his deathbed letter to Hardy and will take place at Vanderbilt University in Nashville, Tennessee on May 18-19 2020. The main theme will be on new developments around the area of partitions, and especially ranks, cranks, and other partition statistics. This conference is oriented at establishing and furthering dialogue on new developments at the boundary of combinatorics and modular forms. This will foster collaboration between researchers working in these fields, and the conference will feature a problem session to delineate and disseminate critical questions, as well as a discussion panel about issues affecting junior and minority researchers. In particular, modular forms and mock modular forms have long been essential tools in the study partitions and other combinatorial sequences. Mock theta functions have led to many results on rank and crank congruences, asymptotics, and inequalities, and conversely, such partition statistics have motivated the development of harmonic Maass forms. Very recently, Stanton has highlighted several conjectures of his and Garvan's in unpublished notes. These conjectures seek a combinatorial refinement of the rank and crank statistics. These suggest a deeper structure both on the combinatorial side and in the mock modular form world. These conjectures have the potential to open up new areas of research at the intersection of combinatorics and mock theta functions. Given these cutting-edge questions and the fitting nature of Ramanujan's anniversary of introducing mock theta functions, it is a particularly opportune time to gather experts from these two fields to discuss the future of such questions and related topics, and to involve the next generation of junior researchers in this conversation and collaboration. Further details can be found on the conference website: https://my.vanderbilt.edu/mock/ This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.