Constantin Teleman (UC Berkeley)”The Quantum GIT conjecture”

Seminar Organizer

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In a landmark work, Frances Kirwan described the relation between the cohomology of a GIT quotient of a smooth projective variety X and the equivariant cohomology of X by what is known as the ‘subtraction method’: this relies on the equivariant perfection of the destabilizing stratification of X. Later work geared toward describing the cohomology ring structure relied on Poincare duality and explicit integration formula, but did not produce explicit answers. It has long been suspected that a better answer applies to quantum cohomology, and a precise conjecture to that effect was proposed by the speaker some time ago. I will describe the background to the conjecture and outline the recent proof, which is joint work with Dan Pomerleano.