This project is a program of fundamental research in Mathematics, more precisely in Algebra, Geometry, and Topology.
Over the past 20 years, the new theory of higher structures (operads, homotopy algebras, infinity-categories) has given rise to powerful tools which made possible the resolution of open problems and prompted revolutions in algebraic topology (faithful algebraic invariants of the homotopy type of spaces), algebraic geometry (derived algebraic geometry), and deformation theory (formal moduli problems) for instance. The purpose of the present project is to apply these higher algebraic methods in order to bring the same kind of groundbreaking developments in algebraic Lie theory, deformation theory, homotopy theory, and discrete/algebraic geometry. The proposed operadic methods are effective and algorithmic, and will thus produce explicit formulas applicable at a wide scale by other mathematicians.
The project is structured over the following four interconnected topics.
The consortium unites experts in each of those fields including permanent faculty members, postdocs and doctoral students.
The project consists of three partners and brings together mathematicians from six universities in France and one university in Spain.
Two one-year research associate positions are funded by this ANR grant, for early career researchers working in areas of algebra, geometry, and topology closely related to this project. One position was be located in Paris (2022-2023) and the other one in Strasbourg (2023-2024).