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BEGIN:VEVENT
SUMMARY:Dmitry Kaledin (Steklov Mathematical Institute\, HSE)
DTSTART:20201217T110000Z
DTEND:20201217T120000Z
DTSTAMP:20260404T092654Z
UID:Noncomgeometry/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Nonco
 mgeometry/1/">Non-commutative cristalline cohomology</a>\nby Dmitry Kaledi
 n (Steklov Mathematical Institute\, HSE) as part of Noncommutative Geometr
 y Conference\n\n\nAbstract\nI am going to give an overview of the several 
 constructions of non-commutative analogs of cristalline cohomology that ap
 peared recently\, with special focus on "linear" constructions of Vologods
 ky-Petrov and Tsygan. If time permits\, I will end with some speculations 
 on what might be possible over $\\mathbb R$.\n
LOCATION:https://stable.researchseminars.org/talk/Noncomgeometry/1/
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BEGIN:VEVENT
SUMMARY:Maxim Kontsevich (IHES)
DTSTART:20201217T130000Z
DTEND:20201217T140000Z
DTSTAMP:20260404T092654Z
UID:Noncomgeometry/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Nonco
 mgeometry/2/">Towards dimension theory for spectral semi-orthogonal decomp
 ositions</a>\nby Maxim Kontsevich (IHES) as part of Noncommutative Geometr
 y Conference\n\n\nAbstract\nIt is expected that the derived category of co
 herent sheaves on a smooth projective variety has a canonical semiorthogon
 al decomposition governed by the generic spectrum of quantum multiplicatio
 n deformed by algebraic classes. I present a hypothetical formula for the 
 Serre dimension of elementary pieces for complete intersections in project
 ive spaces\, and sketch applications to the rationality questions.\n
LOCATION:https://stable.researchseminars.org/talk/Noncomgeometry/2/
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BEGIN:VEVENT
SUMMARY:Denis Auroux (Harvard University)
DTSTART:20201217T143000Z
DTEND:20201217T153000Z
DTSTAMP:20260404T092654Z
UID:Noncomgeometry/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Nonco
 mgeometry/3/">Mirrors of curves and their Fukaya categories</a>\nby Denis 
 Auroux (Harvard University) as part of Noncommutative Geometry Conference\
 n\n\nAbstract\nThe mirror of a genus $g$ curve can be viewed as a trivalen
 t configuration of $3g−3$ rational curves meeting in $2g−2$ triple poi
 nts\; more precisely\, this singular configuration arises as the critical 
 locus of the superpotential in a 3-dimensional Landau-Ginzburg mirror. In 
 joint work with Alexander Efimov and Ludmil Katzarkov\, we introduce a not
 ion of Fukaya category for such a configuration of rational curves\, where
  objects are embedded graphs with trivalent vertices at the triple points\
 , and morphisms are linear combinations of intersection points as in usual
  Floer theory. We will describe the proposed construction of the structure
  maps of these Fukaya categories\, attempt to provide some motivation\, an
 d outline examples of calculations that can be carried out to verify homol
 ogical mirror symmetry in this setting.\n
LOCATION:https://stable.researchseminars.org/talk/Noncomgeometry/3/
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