Compact closed categories, modular operads and loops
May 13, 2021
University of Wollongong
Operator algebra and non-commutative geometry seminar.
Talk on "Compact closed categories, modular operads and loops".
Modular operads are a bit like non-planar versions of Jones’s planar algebras. They are graded systems used to describe moduli spaces of higher genus curves.
Compact closed categories are categories in which every object has a strict dual. For example, the category of finitely generated projective modules and module homomorphisms over a commutative ring is compact closed. I’ll discuss the sense in which duality means we can forget about the direction of morphisms and treat compact closed categories as modular operads, and say something about why this may be useful.
In particular, I will reflect on how to understand some of the challenges involved (the combinatorics of modular operads are complicated!), and whether this approach can tell us anything deeper about notions of genus, trace and duality.