Operadic Deformation Theory

TL;DR

This survey reviews recent advances in algebraic deformation theory, emphasizing the role of algebraic operads and homotopical tools like Koszul duality in understanding deformations of algebraic structures.

Contribution

It provides a comprehensive overview of operadic methods and their applications to deformation problems and formal moduli spaces in algebra.

Findings

Operadic methods effectively analyze algebraic deformations.

Koszul duality is a key tool in the operadic approach.

Applications span various algebraic structures and deformation contexts.

Abstract

This is a survey on recent progress in algebraic deformation theory and the application of algebraic operads to its study. We review the classical homotopical tools in the theory of algebraic operads, namely Koszul duality. We give concrete examples of applications of such tools to various flavours of problems related to deformations of algebraic structures. We also study formal moduli problems and related notions from the operadic point of view.