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A localization formula for Hamiltonian torus actions

Riccardo Ontani
Friday, April 22, 2022 - 14:00 to 15:00

In this talk I will present an ongoing project on Jeffey-Kirwanlocalization in the context of Abelian quiver moduli spaces (or morein general, reduced spaces of suitable Hamiltonian torus actions).In order to motivate the interest in this topic, in the first part ofthe talk I will quickly recall the content of a previous joint workwith Jacopo Stoppa: given a complete bipartite quiver, there is anatural way to construct a log Calabi-Yau surface. In our work we showhow the Gross-Hacking-Keel mirror to this, which is known to encodeboth Gromov-Witten and quiver invariants, can be computed also interms of residues of rational functions, by using a formula of Szenesand Vergne.In the rest of the seminar I will focus on a way to interpret thisformula for the Euler characteristic of a quiver moduli space in termsof the localization procedure due to Jeffrey and Kirwan.

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