BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Ruggero Bandiera (Sapienza Università di Roma)
DTSTART:20240315T140000Z
DTEND:20240315T150000Z
DTSTAMP:20260423T004545Z
UID:ACPMS/36
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ACPMS/36/">C
 umulants\, Koszul brackets and homological perturbation theory for commuta
 tive BVoo and IBLoo algebras</a>\nby Ruggero Bandiera (Sapienza Universit
 à di Roma) as part of Algebraic and Combinatorial Perspectives in the Mat
 hematical Sciences\n\n\nAbstract\nn the first part of this talk we shall r
 eview the classical homotopy transfer theorem in the context of Aoo and Lo
 o algebras. We shall explain how the usual proof of this result for Aoo al
 gebras\, based on the tensor trick and the homological perturbation lemma\
 , can be adapted to Loo algebras using a symmetrized version of the tensor
  trick. In the course of the discussion we shall review the construction o
 f cumulants and Koszul brackets (as well as their coalgebraic analogs): th
 ese are graded symmetric multilinear maps associated respectively to a mor
 phism of graded commutative algebras $f\\colon A \\to B$ or to an endomorp
 hism $d\\colon A \n\\to A$\, measuring the deviation of f from being an al
 gebra morphism in the first case\, and the deviation of d from being an al
 gebra derivation in the second case. A key technical lemma will be that un
 der certain assumptions on the involved contraction\, these are compatible
  with homotopy transfer in an appropriate sense. In the second part of the
  talk we shall review commutative BVoo algebra in the sense of Kravchenko:
  as an application of our previous discussion we shall introduce a new def
 inition of morphisms between these objects in terms of cumulants. Moreover
 \, we shall explain how to use homological perturbation theory to get a ho
 motopy transfer theorem for commutative BVoo algebras\, under certain assu
 mptions on the involved contraction. Finally\, IBLoo algebras\, that is\, 
 commutative BVoo algebras whose underlying algebra is free\, are known to 
 be a model for involutive Lie bialgebras up to coherent homotopies\, and h
 ave recently found several applications in string topology and symplectic 
 field theory. \nAs an application of our results\, we shall explain how to
  obtain a homotopy transfer theorem for IBLoo algebras via the symmetrized
  tensor trick and the homological perturbation lemma.\n
LOCATION:https://researchseminars.org/talk/ACPMS/36/
END:VEVENT
END:VCALENDAR