In 2020, Gukov-Pei-Putrov-Vafa conjectured that Witten-Reshetikhin-Turaev (WRT) invariants are radial limits of homological blocks, which are q-series introduced by them for plumbed 3-manifolds with negative definite linking matrices. In this talk, I prove their
conjecture with three key ideas: (1) To develop a new asymptotic formula by the Euler-Maclaurin summation formula. Then, we can compare asymptotic expansions of WRT invariants and homological blocks; (2) To prove that the conjecture is deduced from the holomorphy of a rational function defined by adding parameters for an expression of WRT invariants; (3) To prove the holomorphy by the induction on pruning of a plumbing graph.
This video was produced by the International Centre for Mathematical Sciences, as part of the workshop Gauge Fields in Arithmetic, Topology & Physics.
