## November 2, 2008

### Higher Structures in Math and Physics in Lausanne

#### Posted by Urs Schreiber

I am about to catch a night train to Lausanne, to attend this workshop:

Higher Structures in Mathematics and Physics 2008
at Bernoulli Center (EPFL) Lausanne, Switzerland
November 3-7, 2008
(program)

Among the other participants, I am looking forward to meeting friend and $n$-Café regular Bruce Bartlett, who recently handed in his PhD thesis and now has time to travel. Hopefully the two of us will manage to report on some of the highlights (and secret highlights) to the 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.)

Posted at November 2, 2008 4:55 PM UTC

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### Re: Higher Structures in Math and Physics in Lausanne

Congratulations on handing in, Bruce! That looks like a great workshop, I look forward to the liveblogging.

Posted by: Jamie Vicary on November 2, 2008 10:42 PM | Permalink | Reply to this

### Re: Higher Structures in Math and Physics in Lausanne

Yes, congratulations Bruce!

Posted by: Tom Leinster on November 3, 2008 12:20 AM | Permalink | Reply to this

This morning we heard Ieke Moerdijk on $\infty$-Categories and $\infty$-Operads (pdf notes).

Posted by: Urs Schreiber on November 3, 2008 10:44 AM | Permalink | Reply to this

Today among the talks was

B. Keller, Periodicity conjecture via 2-Calabi-Yau categories (pdf): there is some complicted combinatorial problem (stemming from a thermodynamic Bethe ansatz to CFT) which can be solved in a nice way be realizing that it is the decategorification of a statement about triangulated categories

and

E. Getzler, TFT in two dimensions and Teichmüller spaces (pdf notes): there is a skeletal filtration of Teichmüller space of punctured Riemann surfaces which implies in one strike various known deep statements about 2d TFTs – as well as a whole series of further statements…

please Notice: The above pdf notes contain the notes I took in real-time in the talks, and I haven’t yet proof read any of this.

Posted by: Urs Schreiber on November 4, 2008 11:10 PM | Permalink | Reply to this

### Re: Higher Structures in Math and Physics in Lausanne

Thanks guys. It’s no joke here at the workshop, there are some high-powered talks but I’m starting to see some hazy picture…I see men, but they look like trees walking.

Posted by: Bruce Bartlett on November 4, 2008 6:35 PM | Permalink | Reply to this
Read the post Lie 3-Algebras on the Membrane (?)
Weblog: The n-Category Café
Excerpt: Recently a trinary bracket appears in the study of the supermembrane which is sometimes addressed as a homotopy algebraic structure.
Tracked: November 7, 2008 1:21 AM

### Re: Higher Structures in Math and Physics in Lausanne

Almost forgot one more set of notes I had taken:

Calin Lazaroiu, TFTs with defects and higher categories (pdf notes)

Posted by: Urs Schreiber on November 24, 2008 9:45 PM | Permalink | Reply to this
Read the post Categories, Logic and Physics in London
Weblog: The n-Category Café
Excerpt: Reporting on the 4th CLP workshop
Tracked: January 8, 2009 10:12 AM