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SUMMARY:Twistor families of categories
DTSTART;VALUE=DATE-TIME:20171211T100000Z
DTEND;VALUE=DATE-TIME:20171211T105000Z
DTSTAMP;VALUE=DATE-TIME:20201025T061422Z
UID:indico-contribution-1687@indico.math.cnrs.fr
DESCRIPTION:Speakers: M. Kontsevich (IHES)\nI will give a definition of a
twistor family (Cζ)\, ζ belonging to the Riemann sphere\, of triangulate
d categories. The propotypical example is the family of derived categories
of coherent sheaves on compact hyperkähler manifold\, endowed with compl
ex structures parametrized by twistor parameter ζ. Another basic example
comes from Simpson's non-abelian Hodge theory. In a joint work (in progres
s) with Y.Soibelman we propose a general approach to twistor families usin
g Fukaya categories associated with holomorphic symplectic manifolds.\n\nT
he most clean case is the product of an elliptic curve and C*. For ζ≠0\
,∞ the corresponding category has a decription in terms of elliptic diff
erence equations. Harmonic objects are solutions of Bogomolony equations o
n 3-dimensional torus with isolated singularities. The universal family of
categories in this example is parametrized by the non-Hausdorff quotient
(CP2 -RP2)/GL(3\; Z).\n\nhttps://indico.math.cnrs.fr/event/2920/contributi
ons/1687/
LOCATION: Amphi Herpin
URL:https://indico.math.cnrs.fr/event/2920/contributions/1687/
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