Gromov-Witten invariants of a smooth projective variety give an infinite tower of cohomology classes on powers of the original variety, satisfying a beautiful system of constraints encoded in the notion of quantum connection.
Recently Hiroshi Iritani proved a result controlling the quantum connection of the blowup along a smooth center.
The goal of the course is to introduce a new class of birational invariants based on Iritani's theorem.
In particular, one can almost effortlessly prove the non-rationality of a generic cubic 4-fold.
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