Download Operations and Configurations Roughly speaking, an `operad` is a

Operations and Configurations
Roughly speaking, an 'operad' is a family of operations, and an 'algebra' for the
operad is an something upon which these operations operate. For example, there is
an associative operad whose algebras are precisely associative algebras. The most
famous examples are the 'little n-discs', whose algebras are things with n different
multiplications commuting 'up to homotopy'.
Operads play an important role in many settings, for example in May's original work
on loopspaces and in Kontsevich's work on deformation quantisation. And very
recently operads have played a role in what is called `chiral homology' or
`factorisation homology', inspired by phenomena in quantum field theory.
I'll give a general introduction to operads, give examples and applications, and then
I'll describe some recent work with David Ayala on chiral homology and the 'Ran
space' of configurations in Euclidean space.