Maurer-Cartan Methods in Deformation Theory

Vladimir Dotsenko is Professor at the University of Strasbourg and Junior Member of the Institut Universitaire de France. His research focuses on homotopical algebra and its applications in areas including category theory, combinatorics and ring theory. Sergey Shadrin is Professor of Geometry and Mathematical Physics at the University of Amsterdam. His main research interests include enumerative geometry, homotopical algebra, integrable hierarchies, and topological recursion. Bruno Vallette is Professor of Mathematics at the Université Sorbonne Paris Nord and was previously Junior Member of the Institut Universitaire de France. He co-authored the book 'Algebraic Operads' (2012) with Jean-Louis Loday, which is now the reference on this topic.

• Introduction; 1. Maurer–Cartan methods; 2. Operad theory for filtered and complete modules; 3. Pre-Lie algebras and the gauge group; 4. The gauge origin of the twisting procedure; 5. The twisting procedure for operads; 6. Operadic twisting and graph homology; 7. Applications.