# Victor Roca Lucio: Postdoc day, Seminar 2: The integration of curved absolute homotopy Lie algebras

**Time: **
Fri 2022-04-01 15.00 - 15.30

**Location: **
Institut Mittag-Leffler, Seminar Hall Kuskvillan and Zoom

**Video link: **
Meeting ID: 921 756 1880

**Participating: **
Victor Roca Lucio (University Paris 13)

**Abstract:** The integration procedure associates an inﬁnity-groupoid to a (complete/nilpotent) homotopy Lie algebra. It dates back to Hinich and Getzler. Recently, a new method was developed by Robert-Nicoud and Vallette: it relies on the representation of the Getzler functor with a universal object. The goal of this talk is to generalize their procedure to curved absolute homotopy Lie algebras. “Absolute algebras” are a new type of algebraic structures that come naturally equipped with inﬁnite summations, without an underlying topology. We will explain how to integrate this new type of objects, generalizing the above cases, and explore their relationship with rational homotopy theory, proving that they provide us with rational models for non-pointed finite type nilpotent spaces.