### Back and Catching Up

#### Posted by Urs Schreiber

After my stay at ESI in Vienna # I spent a week hiking in the Alps with my family. Amazing how much one can miss in one week. Below a list of things I need to catch up with.

The next two weeks I’ll be in Zagreb, visiting Zoran Škoda and Igor Baković with whom we are working on a project on nonabelian differential cohomology (with David Roberts, Hisham Sati and Danny Stevenson). I am hoping to be able to say more about this in a while. Am planning to talk about something at least related at Higher Structures 2008 in November.

Here the list of things to read which I missed last week. And even this list is gonna be incomplete, as I am running out of time…

First of all, my own thread on Planar Algebras, TFTs with Defects. There were a bunch of very useful comments.

As Jens Fjelstad pointed out I should read Subfactors and 1+1-dimensional TQFTs by Kodiyalam, Pati, and Sunder.

As Liang Kong rightly emphasizes , I should blog about Ingo Runkel and Rafal Suszek’s Gerbe-holonomy for surfaces with defect networks.

Then of course The Volume of a Differentiable Stack and especially the stuff that David Ben-Zvi mentions.

Another thing: on the axiomatization of higher categories. Bruce Bartlett kindly wrote in to alert me that somebody here should blog about Eugenia Cheng’s latest Comparing operadic theories of $n$-categories.

Yet another thing: on the axiomatization of quantum field theory. I need to look at the big project by Steve Hollands: Quantum field theory in terms of consistency conditions I: General framework, and perturbation theory via Hochschild cohomology.

And as Jim Stasheff kindly points out, I should blog about the highly interesting new piece by Sergei Gukov and Edward Witten: Branes and Quantization

Abstract:The problem of quantizing a symplectic manifold (M,\omega) can be formulated in terms of the A-model of a complexification of M. This leads to an interesting new perspective on quantization. From this point of view, the Hilbert space obtained by quantization of $(M,\omega)$ is the space of $(B_{cc},B')$ strings, where $B_{cc}$ and $B'$ are two A-branes; $B'$ is an ordinary Lagrangian A-brane, and Bcc is a space-filling coisotropic A-brane. $B'$ is supported on $M$, and the choice of \omega is encoded in the choice of $B_{cc}$. As an example, we describe from this point of view the representations of the group $SL(2,\mathbb{R})$. Another application is to Chern-Simons gauge theory.

More later.

## Re: Back and Catching Up

I was asked by private email about conference recommendations this year and next year. Here are some things I am interested in:

first of all, as mentioned above, I’ll be at

Higher structures 2008, November 3-7, 2008, Lausanne

Then next year:

I’ll be in Oberwolfach June 7-23, 2009, Strings, Fields and Topology

(this is by invitation, but if you are desparate I guess there is still plenty of time to contact the organizers)

Then there is this event which I am hoping to be able to attend at least in parts:

August 3-8 2009, Prague, XVI International Congress on Mathematical Physics

and the sattelite workshop

July 29-31 2009, Göttingen, Algebraic QFT - The first 50 years

Finally, I have just been alerted to apply for Autumn 2009 at the MPI Bonn where Stephan Stolz and Peter Teichner will organize a meeting on functorial field theory. Application requires a PhD, but there are also graduate programs.