BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Slawomir Klimek (Indiana University–Purdue University Indianapol is) DTSTART:20220427T190000Z DTEND:20220427T200000Z DTSTAMP:20260420T052909Z UID:NYC-NCG/100 DESCRIPTION:Title: Smooth subalgebras in noncommutative geometry\nby Slawomir Klimek (I ndiana University–Purdue University Indianapolis) as part of Noncommutat ive geometry in NYC\n\n\nAbstract\nIn noncommutative geometry it is often natural to consider dense *-subalgebras of C*-algebras in particular in co nnection with cyclic cohomology or with the study of unbounded derivations on C*-algebras.\nIf C*-algebras are thought of as generalizations of topo logical spaces\, then dense subalgebras may be regarded as specifying addi tional structures on the underlying space\, like a smooth structure.\nAt p resent there is no universally accepted general theory of such smooth suba lgebras\, however there is a number of "standard" examples defined and stu died in the literature.\nIn analogy with the algebras of smooth functions on a compact manifold\, such a smooth subalgebra should have the following properties:\n(1) It should be closed under holomorphic functional calculu s of all elements and under smooth-functional calculus of self-adjoint ele ments\n(2) It should be complete with respect to a locally convex algebra topology\nThe purpose of the talk is to discuss those concepts on examples \, including some more recent constructions.\n LOCATION:https://researchseminars.org/talk/NYC-NCG/100/ END:VEVENT END:VCALENDAR