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SUMMARY:Unifying Koszul dualities via point-set models
DTSTART:20260623T120000Z
DTEND:20260623T130000Z
DTSTAMP:20260618T092700Z
UID:indico-event-15883@indico.math.cnrs.fr
DESCRIPTION:Speakers: Victor Roca i Lucio\n\nThe classical bar-cobar adjun
 ction between dg algebras and dg coalgebras goes back to the origins of di
 fferential homological algebra as developed by Cartan\, Eilenberg\, Moore\
 , and many others\, and is part of the broader framework of Koszul duality
 . In recent years\, several ∞-categorical analogues of this adjunction h
 ave been developed\, notably by Lurie\, Francis--Gaitsgory\, and Heuts. Ho
 wever\, there is no comparison in the literature between the classical cha
 in-level constructions and their higher-categorical counterparts\, and sur
 prisingly perhaps\, the two constructions are not quite compatible.\nIn th
 is talk\, I will explain who to construct a unified framework relating the
 se different forms of Koszul duality in the differential graded setting. A
 long the way\, I will also explain how giving point-set models for ∞-cat
 egorical types of coalgebras plays a major role in this story. This talk w
 ill be based on two joint works with Dan Petersen and Sinan Yalin.\n\nhttp
 s://indico.math.cnrs.fr/event/15883/
LOCATION:IMT 1R2 207 (Salle Pellos)
URL:https://indico.math.cnrs.fr/event/15883/
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