Theo Backman: Associative algebras up to homotopy

A differential graded associative algebra (A,d) is a differential graded vector space equipped with an associative multiplication m for which the differential is a derivation. It turns out that it is natural to consider the weaker notion of an algebra where the associativity condition is only true up to "homotopy". Such algebras are called A_∞-algebras and they are the topic of this talk.

I will give a self-contained introduction to A_∞-algebras. The talk will cover two or more (as time permits) definitions of A_∞-algebras and a configuration space model of the structure.