Centers in operadic deformation theoryMPIM

by Sonja Maria Farr (MPIM)

Thursday Oct 29, 2026, 3:00 PM → 4:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

MPI-Oberseminar

A formal moduli problem is a space modeling the formal neighborhood of a point in a moduli stack. By the Lurie-Pridham correspondence, every formal moduli problem in characteristic 0 is controlled by a dg Lie algebra. Calaque-Campos-Nuiten proved an operadic version of this correspondence, showing that formal moduli problems parametrized by algebras over a sufficiently nice dg operad correspond to algebras over the Koszul dual operad. A basic example is the deformation theory of an 𝐸_n -algebra . By a result of J. Francis, this is a 𝐸_{n+1} -formal moduli problem controlled by the E_n-Hochschild cohomology of 𝐴, recovering the familiar principle that Hochschild cohomology controls deformations. In this talk I will explain a recent result of mine extending this picture to dg operads, proving that the derived center of an algebra controls its operadic deformation theory