This semester we will read BensonGreenlees paper "Stratifying the derived category of cochains on $BG$ for $G$ a compact Lie group".
Our aim will be study the results and see if we can generalize them to the $p$compact case. The tentative schedule is the following:
1) February 19th. W. Pitsch. Overview 2) March 4th. L. Carlier. Tensor triangualted categories 3) April 1st. T. Lozano. $p$compact groups 4) April 15th. W. Pitsch. Stratification I 5) April 29th. W. Pitsch Stratification II 6) May 6th. J. Kock Pointfree Topology on Spec R and support I 7) May 13rd. J. Kock Pointfree Topology on Spec R and support II 8) May 20th W. Pitsch Some results on D(R) for R a ring spectrum
Date and place: Fridays 12h0013h00, CRM Room A1.
Extraordinary session:
Date and Place: June 9th 12h00, CRM room A1 Speaker: Michael Batanin (Macquarie Univeristy) Title: A less known Deligne's conjecture
Abstract: A now famous Deligne's conjecture on Hochschild cochains (proved by many authors) asserts that this complex is naturally a E_2algebra i.e. an algebra of an operad weakly equivalent to the little 2disk operad. In 1992 Alexey Davydov introduced a construction of a deformation complex of a monoidal functor which reminds the classical Hochschild complex but in many respect is a very different creature. For example, you can apply this construction to the identity functor. The corresponding cohomology classify obstructions for infinitesimal deformations of the associator of a tensor category (like classical Hochschild cohomology classify obstructions for infinitesimal deformations of the multiplication of an associative algebra). So, in some sense, this is a second order or categorification of the Hochschild cohomology. Deligne (in a letter to Davydov in 1993) suggested a simple algebraic condition called ncommutativity for a cosimplicial complex of associative algebras and conjectured that an ncommutative complex has a natural E_{n+1}algebra structure. It can be easily proved that in general Davydov's complex is a 1commutative complex in Deligne's sense but the deformation complex of an identity functor is 2commutative.
Regular seminar:
Date and Place: June 3rd 12h00, CRM room A1 Speaker: Natàlia Castellana (UAB) Title: Noetherianity in cohomology
Abstract: We will show why various cohomologies of interest (pcompact group, plocal groups) have noetherian cohomology. The proofs rest on nice properties of various transfers in these different settings.
