BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ricardo Campos (CNRS - University of Montpellier) DTSTART:20200710T160000Z DTEND:20200710T170000Z DTSTAMP:20260423T035909Z UID:TQFT/9 DESCRIPTION:Title: The homotopy type of associative and commutative algebras\nby Ricardo Cam pos (CNRS - University of Montpellier) as part of Topological Quantum Fiel d Theory Club (IST\, Lisbon)\n\n\nAbstract\nGiven a topological space\, ho w much of its homotopy type is captured by its algebra of singular cochain s? The experienced rational homotopy theorist will argue that one should c onsider instead a commutative algebra of forms. This raises the more algeb raic question "Given a dg commutative algebra\, how much of its homotopy t ype (quasi-isomorphism type) is contained in its associative part?" Despit e its elementary formulation\, this question turns out to be surprisingly subtle and has important consequences.\nIn this talk\, I will show how one can use operadic deformation theory to give an affirmative answer in char acteristic zero.\nWe will also see how the Koszul duality between Lie alge bras and commutative algebras allows us to use similar arguments to deduce that under good conditions Lie algebras are determined by the (associativ e algebra structure of) their universal enveloping algebras.\n\n\n(Joint w ith Dan Petersen\, Daniel Robert-Nicoud and Felix Wierstra and based on ar Xiv:1904.03585)\n LOCATION:https://researchseminars.org/talk/TQFT/9/ END:VEVENT END:VCALENDAR