Explore the fascinating world of birational invariants derived from Gromov-Witten theory in this comprehensive lecture. Delve into the intricate system of constraints governing Gromov-Witten invariants of smooth projective varieties, encoded in the quantum connection. Examine Hiroshi Iritani's groundbreaking theorem on controlling the quantum connection of blowups along smooth centers. Discover a novel class of birational invariants based on Iritani's work, and witness their powerful application in effortlessly proving the non-rationality of generic cubic 4-folds. Join renowned mathematician Maxim Kontsevich from the Institut des Hautes Etudes Scientifiques (IHES) for an illuminating exploration of cutting-edge developments in algebraic geometry and mathematical physics.