Beijing Institute of Mathematical Sciences and Applications

In a sense, the main goal of algebraic topology is the creation of the algebraic description of the category of topological spaces and continuous maps up to homotopy. Rational homotopy theory, developed by Quillen and Sullivan, is a piece of topology where this main goal is completely achievable: homotopy theory of simply connected spaces whose higher homotopy groups are not just abelian groups, but vector spaces over Q, is completely described by their commutative differential graded algebras of cochains, in the sense that there is an equivalence of corresponding localized categories. The goal of this course is to describe this equivalence.