The realm of operads

This talk is an invitation to operads---powerful mathematical tools---applying to all domains of maths (to any symmetric monoidal category), applied maths and mathematical physics. These universal objects, allow to code operations with multiple inputs.

Operads can be considered in very different flavors, ranging from algebra, topology to geometry. In particular, there exists an algebraic operad, ruling associative algebras, a topological operad (little discs), a geometric operad (moduli spaces of curves). The last one codes Gromov—Witten invariants.

Discovered in the 70’s, operads came back into light in the 90’s, due to algebra (Koszul duality), geometry (moduli spaces of curves) and mathematical physics (theory of quantum spaces), under the impulse of Manin and Kontsevitch.