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SUMMARY:Bruno Vallette (Université Sorbonne Paris Nord)
DTSTART:20200811T130000Z
DTEND:20200811T140000Z
DTSTAMP:20260423T004140Z
UID:operad/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/operad/9/">D
 eformation theory of cohomological field theories</a>\nby Bruno Vallette (
 Université Sorbonne Paris Nord) as part of operad pop-up\n\n\nAbstract\nI
  will explain how to develop the deformation theory of cohomological field
  theories as a special case of a general deformation theory of morphisms o
 f modular operads. Two cases will be considered: a classical and a quantum
  one. Using ideas of Merkulov–Willwacher based on graphs complexes\, I w
 ill introduce and develop a new universal deformation group which acts fun
 ctorially via explicit formulas on the moduli spaces of gauge equivalence 
 classes of morphisms of modular operads. In the classical case\, the actio
 n is trivial\; but in the quantum case\, this group contains the prounipot
 ent Grothendieck–Teichmüller group and its action is highly non-trivial
  even in the simplest case. Then\, I will enrich these graph complexes wit
 h characteristic classes coming from the geometry of the moduli spaces of 
 curves and obtain in this way (rather surprisingly) a natural homotopy ext
 ension to Givental group action in the classical case\, and in the quantum
  case\, a huge group that includes both Givental and Grothendieck–Teichm
 üller groups. \n\nIt is a joint work with Volodya Dotsenko\, Sergey Shadr
 in\, and Arkady Vaintrob (arXiv:2006.01649).\n
LOCATION:https://researchseminars.org/talk/operad/9/
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