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BEGIN:VEVENT
SUMMARY:Dmitry Kaledin (Steklov Mathematical Institute\, HSE)
DTSTART:20201217T110000Z
DTEND:20201217T120000Z
DTSTAMP:20260422T212609Z
UID:Noncomgeometry/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Noncomgeomet
 ry/1/">Non-commutative cristalline cohomology</a>\nby Dmitry Kaledin (Stek
 lov Mathematical Institute\, HSE) as part of Noncommutative Geometry Confe
 rence\n\n\nAbstract\nI am going to give an overview of the several constru
 ctions of non-commutative analogs of cristalline cohomology that appeared 
 recently\, with special focus on "linear" constructions of Vologodsky-Petr
 ov and Tsygan. If time permits\, I will end with some speculations on what
  might be possible over $\\mathbb R$.\n
LOCATION:https://researchseminars.org/talk/Noncomgeometry/1/
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BEGIN:VEVENT
SUMMARY:Maxim Kontsevich (IHES)
DTSTART:20201217T130000Z
DTEND:20201217T140000Z
DTSTAMP:20260422T212609Z
UID:Noncomgeometry/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Noncomgeomet
 ry/2/">Towards dimension theory for spectral semi-orthogonal decomposition
 s</a>\nby Maxim Kontsevich (IHES) as part of Noncommutative Geometry Confe
 rence\n\n\nAbstract\nIt is expected that the derived category of coherent 
 sheaves on a smooth projective variety has a canonical semiorthogonal deco
 mposition governed by the generic spectrum of quantum multiplication defor
 med by algebraic classes. I present a hypothetical formula for the Serre d
 imension of elementary pieces for complete intersections in projective spa
 ces\, and sketch applications to the rationality questions.\n
LOCATION:https://researchseminars.org/talk/Noncomgeometry/2/
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BEGIN:VEVENT
SUMMARY:Denis Auroux (Harvard University)
DTSTART:20201217T143000Z
DTEND:20201217T153000Z
DTSTAMP:20260422T212609Z
UID:Noncomgeometry/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Noncomgeomet
 ry/3/">Mirrors of curves and their Fukaya categories</a>\nby Denis Auroux 
 (Harvard University) as part of Noncommutative Geometry Conference\n\n\nAb
 stract\nThe mirror of a genus $g$ curve can be viewed as a trivalent confi
 guration of $3g−3$ rational curves meeting in $2g−2$ triple points\; m
 ore precisely\, this singular configuration arises as the critical locus o
 f the superpotential in a 3-dimensional Landau-Ginzburg mirror. In joint w
 ork with Alexander Efimov and Ludmil Katzarkov\, we introduce a notion of 
 Fukaya category for such a configuration of rational curves\, where object
 s are embedded graphs with trivalent vertices at the triple points\, and m
 orphisms are linear combinations of intersection points as in usual Floer 
 theory. We will describe the proposed construction of the structure maps o
 f these Fukaya categories\, attempt to provide some motivation\, and outli
 ne examples of calculations that can be carried out to verify homological 
 mirror symmetry in this setting.\n
LOCATION:https://researchseminars.org/talk/Noncomgeometry/3/
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