Modularity and Quantum Topology

The event titled 'Modularity and Quantum Topology' will take place at the American Institute of Mathematics in Pasadena, United States. This workshop focuses on the emerging interactions between modular forms and quantum topology, as well as their connections to related areas including representation theory, combinatorics, and mathematical physics. The primary motivation for this workshop is grounded in foundational work by notable researchers such as Lawrence and Zagier, Witten, and Habiro, alongside recent advances at the intersection of modular forms and knot theory. Key topics of discussion will include the Volume and Modularity Conjectures and Nahm's conjecture concerning the modularity of certain hypergeometric series. Additional focal points will cover quantum and holomorphic quantum modular forms, properties of the Habiro ring, and the concept of resurgence.The workshop aims to bring together researchers at various career stages to collaboratively tackle related problems from diverse mathematical perspectives. Participants will be invited to propose open problems and questions prior to the workshop, which will then be shared on the workshop website. These will include specific challenges that may yield progress during the event, as well as more ambitious inquiries that could shape future developments in the field. Lectures will be aimed at providing participants with the background material necessary for engaging with these problems, and the schedule will also feature discussion sessions and parallel working groups. The event has space and funding available for a limited number of additional participants.