Homological perturbation theory for cyclic L-infinity algebrasMPIM

by Ezra Getzler (Northwestern University)

Monday Sep 14, 2026, 2:00 PM → 3:00 PM Europe/Berlin

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

MPIM Topology Seminar

Homological perturbation theory is a way of transporting algebraic structures from a complex to a homotopy retract. For example, a homotopy retract of a dg algebra has a canonical A-infinity structure (under suitable convergence hypotheses), and a homotopy retract of a dg Lie algebra has a canonical L-infinity structure. There is also a canonical A-infinity/L-infinity morphism from the original dg (Lie) algebra to its homotopy retract.

The problem I address in this talk, motivated by questions in mathematical physics, is to extend this story to cyclic L-infinity algebras: according to Kontsevich, these are essentially the same thing as symplectic formal derived stacks, and the variant of homological perturbation theory that I will explain has a differential geometric flavour, since it is based on integrating a vector field on this derived stack.

Time permitting, I will mention how to carry out similar arguments in the associative, and commutative, settings. In fact, all of these constructions extend to algebras over a cyclic Koszul operad.

I will not assume prior familiarity with L-infinity algebras, or homological perturbation theory.