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DTSTART;TZID=America/New_York:20251002T160000
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CREATED:20250904T162108Z
LAST-MODIFIED:20250926T180606Z
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SUMMARY:Special Kähler geometry and collapsing
DESCRIPTION:Differential Geometry and Physics Seminar  \nSpeaker: Valentino Tosatti\, NYU Courant Institute \nTitle: Special Kähler geometry and collapsing \nAbstract: Special Kähler geometry was first discovered in the context of N=2 supersymmetric 4D gauge theories\, and it also plays a prominent role in mirror symmetry. A key observation of Donagi-Witten and Freed is that the base of every algebraic integrable system admits a special Kähler metric\, while the total space admits a hyperkähler metric. In this talk I will consider compact hyperkähler manifolds with a an algebraic integrable system (i.e. a holomorphic Lagrangian torus fibration)\, and consider a family of hyperkähler metrics such that the volume of the torus fibers shrinks to zero. I will explain how the hyperkähler metrics must collapse to a special Kähler metric on the base (away from the discriminant locus)\, and what we can say about the metric completion of the limit. \n 
URL:https://cmsa.fas.harvard.edu/event/dgphys_10225/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Differential Geometry and Physics Seminar
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