This monograph provides an overview on the Maurer-Cartan methods in algebra, geometry,
topology, and mathematical physics. It offers a conceptual, exhaustive and gentle treatment …

Covering an exceptional range of topics, this text provides a unique overview of the Maurer-
Cartan methods in algebra, geometry, topology, and mathematical physics. It offers a new …

This paper provides a conceptual study of the twisting procedure, which amounts to create
functorially new differential graded Lie algebras, associative algebras or operads (as well as …

Given a holomorphic family of Bridgeland stability conditions over a surface, we define a
notion of spectral network which is an object in a Fukaya category of the surface with …

We develop the basic theory of curved A_ ∞ A∞-categories (cA_ ∞ c A∞-categories) in a
filtered setting, encompassing the frameworks of Fukaya categories (Fukaya et al. in Part I …

We present a homotopy theory for the category of modules over a curved A∞-algebra over a
commutative unital ring. We give a functorial construction of a unital curved dga called the …