BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Aleksandar Milivojevic (Max Planck Institute for Mathematics - Bon n) DTSTART:20220621T150000Z DTEND:20220621T160000Z DTSTAMP:20260423T022624Z UID:Geolis/90 DESCRIPTION:Title: Holomorphic notions of formality and Massey products\nby Aleksandar Mi livojevic (Max Planck Institute for Mathematics - Bonn) as part of Geometr ia em Lisboa (IST)\n\n\nAbstract\nI will discuss joint work with Jonas Ste lzig in which we consider the beginnings of a bigraded analogue of rationa l homotopy theory adapted to complex manifolds\, in a somewhat different f ashion than that of Neisendorfer-Taylor which appeared in the 1970’s soo n after Sullivan’s Infinitesimal Computations in Topology. Taking cues f rom an additive decomposition theorem for double complexes\, we define two natural notions of formality for our basic objects — commutative bigrad ed bidifferential algebras — which place both bigraded components of the de Rham differential on equal footing. These notions are related by the d dbar-lemma (the additive property used to show formality\, in the usual se nse\, of compact complex manifolds admitting a Kähler metric). We conside r obstructions to these notions of formality\, taking in Bott-Chern cohomo logy classes and outputting classes in a chain complex of Demailly-Schweit zer\, whose construction mimics those of classical Massey products and ext ends the triple products landing in Aeppli cohomology considered by Angell a-Tomassini\; we also touch upon their behavior under blow-ups and more ge nerally positive-degree holomorphic maps.\n LOCATION:https://researchseminars.org/talk/Geolis/90/ END:VEVENT END:VCALENDAR