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The Quantum GIT conjecture
December 12, 2024 @ 10:00 am - 11:00 am
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Mathematical Physics and Algebraic Geometry Seminar
Speaker: Daniel Pomerleano (UMass Boston)
Title: The Quantum GIT conjecture
Abstract: Let X be a Fano variety with G action. The quantum GIT conjecture predicts a formula for the quantum cohomology of “anti-canonical” GIT quotients X//G in terms of the equivariant quantum cohomology of X. The formula is motivated by ideas from 3- dimensional gauge theory (“Coulomb branches”) and provides a vast generalization of Batyrev’s formula for the quantum cohomology of a toric Fano variety. I will describe our ongoing work with C. Teleman proving this conjecture. Along the way, I will also discuss integral versions of certain classical facts in the theory of Hamiltonian G-manifolds which are of independent interest.