13/07/2011, 15:30 — 16:30 — Room P3.10, Mathematics Building
João Faria Martins, Univ. Nova de Lisboa
Categorifying the Knizhnik-Zamolodchikov connection
(Joint with Lucio Simone Cirio, Max Planck Institute for Mathematics)
In the context of higher gauge theory, we categorify the Knizhnik-Zamolodchikov connection in the configuration space of particles in the complex plane by means of a differential crossed module of (totally symmetric) horizontal 2-chord diagrams, categorifying the 4-term relation.
We carefully discuss the representation theory of differential crossed modules in chain-complexes of vector spaces, inside which we formulate the notion of infinitesimal 2-R matrix, an infinitesimal counterpart of some of the relations satisfied by braid cobordisms.
We present several open problems.