Seminar: Emanuele Pavia - Categorification of Koszul duality in algebraic topology (Jan 20, 2026)

Speaker: Emanuele Pavia (Université du Luxembourg and SISSA-Trieste)
Title: Categorification of Koszul duality in algebraic topology
Time: January 20, 2026 at 18:00 Istanbul local time (16:00 Trieste/Esch-sur-Alzette local time).
Place: Online
Meeting ID: 935 6390 4955
Passcode: 699568
Abstract: It is well known that for a pointed topological space X both the singular chains on its n-fold loop space C_∙(Ω_*^nX) and its singular cochains C^∙(X) are En-algebras. When X is sufficiently nice and the ground ring is a field, then these E_n-algebras are Koszul dual: for n=1, this means that they are Koszul dual associative algebras. In this latter case, Beilinson, Ginzburg and Soergel proved that their bounded derived categories are equivalent. In this talk, we will see how a similar statement holds for all integers n≥2 after considering categorified modules over the En-algebras C_∙(Ω_*^nX) and C^∙(X). These arise geometrically as higher categories of quasi-coherent sheaves over two (inequivalent) derived stacks, both associated to the topological space X .
This is based on joint work with James Pascaleff and Nicolò Sibilla.