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SUMMARY:Higher Koszul duality for modules in algebraic topology
DTSTART:20251216T130000Z
DTEND:20251216T140000Z
DTSTAMP:20260504T084600Z
UID:indico-event-14887@indico.math.cnrs.fr
DESCRIPTION:Speakers: Emanuele Pavia (Université du Luxembourg)\n\nMany p
 henomena concerning dualities between algebraic structures can be understo
 od as manifestations of Koszul duality. For example\, when X is a (reasona
 ble) topological space X\, the algebra of singular chains on its n-fold lo
 op space $C_*(\\Omega^nX)$ and the algebra of singular cochains $C^*(X)$ a
 re $E_n$-Koszul dual. On another note\, bounded derived categories of Kosz
 ul dual associative ($E_1$-)algebras are known to be equivalent.\nIn this 
 talk\, we will generalize this latter picture for arbitrary n ⩾ 2 by con
 sidering categorified modules over the $E_n$-algebras $C_*(\\Omega^nX)$ an
 d $C^*(X)$. These arise geometrically as higher categories of quasi-cohere
 nt sheaves over two inequivalent derived stacks associated to the topologi
 cal space X. This is based on joint work with J. Pascaleff and N. Sibilla.
 \n\nhttps://indico.math.cnrs.fr/event/14887/
LOCATION:IMT 1R2 207 (Salle Pellos)
URL:https://indico.math.cnrs.fr/event/14887/
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