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SUMMARY:Bridgeland Stability over Non-Archimedean Fields
DTSTART;VALUE=DATE-TIME:20190314T133000Z
DTEND;VALUE=DATE-TIME:20190314T153000Z
DTSTAMP;VALUE=DATE-TIME:20200811T124035Z
UID:indico-event-4427@indico.math.cnrs.fr
DESCRIPTION:Bridgeland stability structure/condition on a triangulated cat
egory is a vast generalization of the notion of an ample line bunlde (or p
olarization) in algebraic geometry. The origin of the notion lies in strin
g theory\, and is applicable to derived categories of coherent sheaves\, q
uiver representations and Fukaya categories. In a category with Bridgeland
stability every objects carries a canonical filtration with semi-stable p
ieces\, an analog of Harder-Narasimhan filtration.\n\nIt is expected that
for categories over complex numbers Bridgeland stability structures often
admit analytic enhancements\, similar to the relation between ample bundle
s and usual Kaehler metrics. In a sense\, this should be a generalization
Donaldson-Uhlenbeck-Yau theorem which syas that a holomorphic vector bundl
e over compact Kaehler manifold is polystable if and only if it admits a m
etrization satisfying hermitean Yang-Mills equation.\n\nIn my course I wil
l talk about a non-archimedean analog of analytic Bridgeland stability. I
will show several examples\, results and conjectures. In particular\, I'll
introduce non-archimedean moment map equations\, generalized honeycomb di
agrams\, and hypothetical stability on derived categories of coherent shea
ves on maximally degenerating varieties over non-archimedean fields. \n\nh
ttps://indico.math.cnrs.fr/event/4427/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/4427/
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