Andrey Lazarev:Minimal models for algebras over operads
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.