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SUMMARY:Julian Holstein (University of Hamburg\, Germany)
DTSTART:20250226T130000Z
DTEND:20250226T140000Z
DTSTAMP:20260423T005753Z
UID:LAGOON/100
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LAGOON/100/"
 >Curvature\, Koszul duality and Calabi–Yau structures</a>\nby Julian Hol
 stein (University of Hamburg\, Germany) as part of Longitudinal Algebra an
 d Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nI will talk about t
 wo aspects of Koszul duality. Firstly\, Koszul duality for dg categories p
 rovides a way of modelling dg categories as certain curved coalgebras. Thi
 s is a linearization of the correspondence of simplicial categories as sim
 plicial sets (quasi-categories) and curved coalgebras have better formal p
 roperties than dg categories. Secondly\, Koszul duality exchanges two self
 -dualities: smooth and proper Calabi–Yau structures. This is a generaliz
 ation and conceptual explanation of the following phenomenon: For a topolo
 gical space X with the homotopy type of a finite complex having an oriente
 d Poincaré duality structure (with local coefficients) is equivalent to h
 aving a smooth Calabi–Yau structure on the dg algebra of chains on the b
 ased loop space of X. A similar phenomenon occurs for Lie algebras. This i
 s joint work with Andrey Lazarev and with Manuel Rivera\, respectively.\n\
 nhttps://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PU
 T09\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON\n
LOCATION:https://researchseminars.org/talk/LAGOON/100/
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