Andrey Lazarev:Minimal models for algebras over operads

Abstract: I will present a general result stating that under very general assumptions an algebra over a differential graded operad admits a minimal model, i.e. one that has vanishing differential. This minimal model is unique up to a non-canonical isomorphism. There is also the corresponding result for modular operads. The structure maps are expressed in terms of trees (or general Feynman diagrams in the modular case) resembling the quasi-classical approximation of Feynman path integrals. This result generalizes and gives a conceptual explanation of an old result of Kadeishvili, and also of more recent formulas due to Kontsevich-Soibelman and Merkulov. This is a joint work with J. Chuang.