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Geometry and Physics Seminar
Flops of any length, Gopakumar-Vafa invariants and 5d Higgs Branches
Flops of any length, Gopakumar-Vafa invariants and 5d Higgs Branches
Organizers
Hamed Adami
,
Chi Ming Chang
,
Mohammad Yavartanoo
Speaker
Andrés Collinucci
Time
Thursday, December 15, 2022 4:00 PM - 5:00 PM
Venue
1131
Online
Zoom 293 812 9202
(BIMSA)
Abstract
The conifold, the primal example of a simple flop of length one, has been a go-to example for thought experiments in string theory for decades: From creating quiver gauge theories, to computing Gopakumar-Vafa invariants of Calabi-Yau threefolds. It has two features that make it extremely workable: It is a hypersurface, it is toric. Over the past decade, mathematicians have created a zoology of examples where the toricity assumption is dropped. These are singular varieties that still admit simple flops, but can not be described via toric methods. Nevertheless, a lot is known about them thanks to the Noncommutative Crepant Resolutions programme. In this talk, I will present an original method for studying these varieties and computing their genus-zero Gopakumar-Vafa invariants based on a new string-theoretic interpretation that involves M-theory/IIA duality. I will give a basic introduction to simultaneous resolutions, and then present these findings.