The n-Category Café

My talk will follow these notes here:

Differential nonabelian cohomology
(pdf, 6 pages plus a bit of extra stuff)

Abstract. Nonabelian cohomology generalizes Čech cohomology with coefficients in sheaves of complexes of abelian groups to cohomology with coefficients in sheaves of $\infty$-categories. It classifies in particular higher principal bundles and their higher gerbes of sections. There is a differential version which classifies higher bundles with connection. Classes of examples of these arise from possibly twisted lifts of structure groups through shifted central String-like extensions. Using $\infty$-Lie theory relating smooth $\infty$-groupoids and $\infty$-Lie-algebroids we construct twisted String 2- and twisted Fivebrane 6-bundles as well as their obstructing Chern-Simons 3- and 7-bundles. We explain the Green-Schwarz mechanism and its magnetic dual version from this point of view.

The exposition is based on work in preparation with Hisham Sati, Zoran Škoda and Danny Stevenson, which among other things provides an $\infty$-frame for my work with Konrad Waldorf and much of the previous stuff.

(At the time this post goes online the above pdf is still in need of some polishing, which I’ll do tonight on the train.)