Quantum modular forms from three-manifolds
Miranda Cheng (Amsterdam)
Title: Quantum modular forms from three-manifolds
Abstract: Quantum modular forms are functions defined on rational numbers that have rather mysterious weak modular properties. Mock modular forms and false theta functions are examples of holomorphic functions on the upper-half plane which lead to quantum modular forms. Generalising the Witten-Reshetikhin-Turaev invariants, a new topological invariants named homological blocks for (in particular plumbed) three-manifolds have been proposed a few years ago. My talk aims to explain the recent observations on the quantum modular properties of the homological blocks, as well as the relation to logarithmic vertex algebras. The talk will be based on a series of work in collaboration with Sungbong Chun, Boris Feigin, Francesca Ferrari, Sergei Gukov, Sarah Harrison, and Gabriele Sgroi.
Recording taken from the Arithmetic Geometry and Quantum Field Theory seminar, organised by Jeff Harvey and Minhyong Kim