Higher Koszul duality for modules in algebraic topology

par Emanuele Pavia (Université du Luxembourg)

mardi 16 déc. 2025, 14:00 → 15:00 Europe/Paris

IMT 1R2 207 (Salle Pellos)

Many phenomena concerning dualities between algebraic structures can be understood as manifestations of Koszul duality. For example, when X is a (reasonable) topological space X, the algebra of singular chains on its n-fold loop space $C_*(\Omega^nX)$ and the algebra of singular cochains $C^*(X)$ are $E_n$-Koszul dual. On another note, bounded derived categories of Koszul dual associative ($E_1$-)algebras are known to be equivalent.

In this talk, we will generalize this latter picture for arbitrary n ⩾ 2 by considering categorified modules over the $E_n$-algebras $C_*(\Omega^nX)$ and $C^*(X)$. These arise geometrically as higher categories of quasi-coherent sheaves over two inequivalent derived stacks associated to the topological space X. This is based on joint work with J. Pascaleff and N. Sibilla.