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SUMMARY:Differential Forms for Smooth Affine Algebras over Operads
DTSTART:20201124T101500
DTEND:20201124T111500
DTSTAMP:20260415T211045Z
UID:d5d55ea5275e1b4102c660c3eb72c39d4984d790a9ebd2ecabefcf2f
CATEGORIES:Conferences - Seminars
DESCRIPTION:Pedro Tamaroff\, Trinity College Dublin\nThe Hochschild--Kosta
 nt--Rosenberg theorem is a classical algebro-geometric result: Hochschild 
 homology and cohomology of a smooth commutative algebra can be computed as
  the space of differential forms and of poly-vector fields on it\, respect
 ively. It says\, in other words\, how to compute the cohomology of a commu
 tative algebra if we pull it back through the canonical projection of oper
 ads p : Ass --> Com and consider it merely to be associative. This result 
 was then exploited to study the deformation theory of smooth commutative a
 lgebras\, and obtain the celebrated Kontsevich formality theorem (cf. D. T
 amarkin's proof). In this talk\, I will explain how to answer the followin
 g natural generalization of this question: given a map of operads f : P --
 > Q and a smooth Q-algebra A\, how can one construct a space Ω*(A) of 'di
 fferential forms for A' and when can one produce an isomorphism from the (
 Hochschild) homology of the pullback P-algebra A to Ω*(A)? In particular\
 , I'll explain how to recover the usual Hochschild--Kostant--Rosenberg the
 orem using operadic homological algebra. This is joint work with Ricardo C
 ampos (IMAG\, Universite Montpellier\, CNRS)\, arXiv:2010.08815.
LOCATION:World Wide Web https://epfl.zoom.us/j/94351048760
STATUS:CONFIRMED
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