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SUMMARY:Operations on Hochschild complexes\, revisited - Tsygan\, B (North
 western University)
DTSTART:20130402T153000Z
DTEND:20130402T163000Z
UID:TALK44268@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Algebraic structures on Hochschild cochain and chain complexes
  of algebras are long known to be of considerable interest. On the one han
 d\, some of them arise as standard operations in homological algebra. On t
 he other hand\, for the ring of functions on a manifold\, Hochschild homol
 ogy\, resp. cohomology\, is isomorphic to the space of differential forms\
 , resp. multivector fields\, and many algebraic structures from classical 
 calculus can be defined (in a highly nontrivial way) in a more general set
 ting of an arbitrary algebra and its Hochschild complexes. Despite an exte
 nsive amount of work on the subject\, it appears that large parts of the a
 lgebraic structure on the Hochschild complexes of algebras and their tenso
 r products are still unknown. I will review the known results (Kontsevich-
 Soibelman\, Dolgushev\, Tamarkin and myself\, Keller) and then outline som
 e provisional results and conjectures about new operations. The talk will 
 not assume any prior knowledge beyond the basic facts about complexes and 
 (co)homology.\n
LOCATION:Seminar Room 1\, Newton Institute
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