### Waldorf on *Transport Functors and Connections on Gerbes*

#### Posted by Urs Schreiber

Konrad Waldorf used to be a PhD student in Hamburg until recently and has now moved to Berkeley. Upon arrival there he has now given two talks on our joint work on parallel 2-transport. You can find nicely readable slides of his talks on his website

Konrad Waldorf
*Connections on non-abelian gerbes and their holonomy*

(pdf slides part I, part II)

As $n$-Café-regulars know, this is based on our series of joint articles

U. S., K. W.
*Parallel transport and functors*

(blog, arXiv)
*Smooth 2-functors and differential forms*

(blog, arXiv)
*Connections on nonabelian gerbes and their holonomy*

(blog, arXiv)

which in turn goes back to my joint work with John Baez

J. B. , U.S.
*Higher gauge theory*

(blog, arXiv)

and my thesis (blog, arXiv), where the diagrams for 2-holonomy first appeared, which we now identified as cells in the codescent 2-groupoid (the 2-groupoid of “2-paths in the Čech 2-groupoid”) and describe in precise detail. I had already talked about the basic idea in Vietri 05, where I also met Roger Picken whose work

M. Mackaay, R. Picken
*Holonomy and parallel transport for abelian gerbes*

(arXiv)

was very influential for the development of *Higher gauge theory* (John Baez’s review page) aka *nonabelian differential cohomology* (lecture notes).

Just recently Roger Picken with João Martins followed up on this in the non-abelian context

J. Martins, R. Picken
*On two-dimensional holonomy*

(arXiv)
*Cubical 2-bundles with connection and Wilson spheres*

(arXiv)

They use the cubical model for 2-groupoids where we use the globular one, but our two discussions of nonabelian differential cocycles are otherwise pretty close.

## Re: Waldorf on Transport Functors and Connections on Gerbes

Does Konrad plan to work with someone in particular at Berkeley? Teichner, I guess?