Literature
J.-L. Loday, B.Vallette "Algebraic Operads"
M. Markl, S. Schnider, J. Stasheff "Operads in Algebra, Topology and Physics" No. 96. American Mathematical Soc., 2007.
V.Ginzburg, and M.Kapranov."Koszul duality for operads." Duke mathematical journal 76.1 (1994): 203-272.
J.P.May, "The geometry of iterated loop spaces, volume 271 of Lecture Notes in Mathematics." (1972).
J.Boardman, and R. Vogt. "Homotopy invariant algebraic structures on topological spaces". Vol. 347. Springer, 2006.
B.Keller "Introduction to A-infinity algebras and modules" arXiv:9910179
Polishchuk, A., & Positselski, L. (2005). Quadratic algebras (Vol. 37). American Mathematical Soc..
General information
There will be a home exam based on some exercises formulated during the talks and some exercises posted in exercise sheets.
Exercises and Problems
Examples of algebraic operads (english version) (русская версия)
Koszul duality and more homological algebra
Exam is a home exam. Deadline -- Dec 24.
12/09 Introduction (A.Khoroshkin)
19/09 Nonsymmetric and Symmetric operads: definitions and examples (A.Khoroshkin)
26/09 More examples and computations of Symmetric operads (A.Khoroshkin)
03/10 Resolutions, Bar-cobar resolution, A_{\infty}-algebras (A.Khoroshkin)
10/10 Stasheff polytopes (A.Khoroshkin)
17/10 P_\infty-algebras and P_\infty morphisms (A.Khoroshkin)
24/10 Homotopy Trasfer for complexes (A.Khoroshkin)
31/10 Homotopy transfer for algebras over an operad (A.Khoroshkin)
07/11 Rational homotopy type (A. Gorinov)
14/11 Loop spaces and modules over Associahedron operad (A.Gorinov)
21/11 Closed Model Categories (sketch by A.Gorinov)
28/11 Building is closed! No lecture, celebrating HSE Anniversary
05/12 Model categories for algebras over an operad (A.Khoroshkin)
12/12 Koszul duality for algebras and for operads (A.Khoroshkin)