QK = GV, two integral invariants on Calabi--Yau threefolds


On Calabi–Yau threefolds there are two types of integral invariants, quantum K-invariants and Gopakumar–Vafa invariants. In this talk, I will explain a joint project (with You-Cheng Chou) which aims to show that the quantum K-invariants and Gopakumar invariants are equivalent. At genus zero, this is a conjecture by Jockers–Mayr and Garoufalidis–Scheidegger (for the quintic), and a proof of the JMGS conjecture will be presented.