Introduction of the course

Information

This course is divided in three parts. In the first part, I explain the general definition of an operad and the applications of operads to the definition of categories of algebras. In the second part, I explain the applications of operads to the definition of homotopy commutative algebra structures on cochain complexes that underlie the classical commutative algebra structures of the cohomology of topological spaces. In the third part, I tackle applications of these homotopy commutative algebra to the definition of models of the homotopy theory of spaces, which extend the classical Sullivan model of the rational homotopy theory of spaces.

The course, available on moodle (see above), comprises series of recorded lectures, accompanying notes and exercices.