Explore the fascinating world of birational invariants derived from Gromov-Witten theory in this comprehensive 2-hour lecture by renowned mathematician Maxim Kontsevich at the Institut des Hautes Etudes Scientifiques (IHES). 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. Gain valuable insights into advanced mathematical concepts at the intersection of algebraic geometry and quantum cohomology.