Operads: exercise session Seminar Room 1, Newton Institute An
operad is an algebraic device which encodes a type of algebras.
Instead of studying the properties of a particular algebra, we
focus on the universal operations that can be performed on the
elements of any algebra of a given type. The information
contained in an operad consists in these operations and all the
ways of composing them. The notion of an operad is a universal
tool in mathematics and operadic theorems have been applied to
prove results in many different fields. The aim of this course
is, first, to provide an introduction to algebraic operads,
second, to give a conceptual treatment of Koszul duality, and,
third, to give applications to homotopical algebra. An operad is
a mathematical object which allows us to encode the operations
acting on categories of algebras. In this course, we will define
the notion of operad together with many examples. We will then
develop the homological algebra for operads leading to the
Koszul duality theory. W