This workshop, sponsored by AIM and the NSF, will be devoted to emerging interactions between modular forms and quantum topology along with their connections to related areas such as representation theory, combinatorics, and mathematical physics. The workshop's primary motivation stems from foundational work of Lawrence and Zagier, Witten, Habiro, and others, as well as recent advances at the intersection of modular forms and knot theory, e.g., the Volume and Modularity Conjectures. Further motivating developments include Nahm’s conjecture on the modularity of certain $q$-hypergeometric series, quantum and holomorphic quantum modular forms, properties of the Habiro ring, and resurgence. An important goal of the workshop is to bring together researchers at various career stages to collaboratively work on related problems from complementary mathematical perspectives.

The main topics for the workshop include

• Volume and Modularity Conjectures
• Habiro ring and colored Jones polynomials, identities, resurgence, and (holomorphic) quantum modularity
• The interplay among q-hypergeometric series, modular forms, representation theory, and combinatorics