EVENT DETAILS AND ABSTRACT

Title: Operads, modules and topological field theory
Speaker: Geoffroy Horel
Speaker Info: MIT
Brief Description:
Special Note:
Abstract:

In this talk I will describe a general theory of modules over an algebra over an operad. Specializing to the operad E_d of little d-dimensional disks, I will show that each d-1 manifold gives rise to a theory of modules. I will then describe a geometric construction of the homomorphisms objects in these categories of modules inspired by factorization homology (also called chiral homology). One particular case is higher Hochschild cohomology (i.e. Hochschild cohomology for E_d-algebras). This construction enlightens the relationship between Hocshchild cohomology and geometric obejcts like the cobordism category and the spaces of long knots.