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BEGIN:VEVENT
DTSTAMP:20251118T131251Z
DTSTART:20251208T150000Z
DTEND:20251208T160000Z
SUMMARY:Manchester Geometry Seminar - Dmitry Roytenberg
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}l17l-mi4lfw
 tl-ft2ar7
DESCRIPTION:Speaker: Dmitry Roytenberg (Amsterdam)\n\nTitle: On dg-manifo
 lds with vanishing Atiyah class\n\nAbstract:\n\nDifferential graded (dg)
  manifolds are a generalization of manifolds comprising and combining (h
 igher) Lie algebroids\, on the one hand\, and derived manifolds on the o
 ther. DG manifolds are objects of a homotopy theory\, in the sense of th
 ere being a natural notion of equivalence between them that is weaker th
 an that of an isomorphism (but reducing to isomorphism when the dg-struc
 ture is trivial). In this context it is natural to look for invariants o
 f dg-manifolds under the weak equivalence. Among suitable candidates for
  such invariants are characteristic classes\, of which one of the best k
 nown examples is the Atiyah class\, which obstructs the existence of an 
 affine connection compatible with the dg-structure. This class was first
  defined for general dg-manifolds by Shoikhet and has since then been st
 udied by a number of authors\, particularly in connection with deformati
 on quantization and gauge theory. It turns out that the vanishing of the
  Atiyah class -- that is\, the existence of a compatible connection -- i
 mposes stringent regularity conditions on the dg-manifold in question. I
 n particular\, such a dg-manifold is necessarily\, in a suitable sense\,
  locally trivial\, so that the global condition becomes purely topologic
 al (in case of foliations\, one recovers Molino's results of the early 1
 970's). This talk is based on joint work in progress with Thanasis Chatz
 istavrakidis and Lara Jonke.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams Room 1\, Alan Turing Building\, Manchester
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