Results from NCG + LQG workshop in Feb 2010 at Oberwolfach

[marcus]

The workshop involved some top people including Mathilde Marcolli (longtime co-author with Alain Connes), Jerzy Lewandowski, Thomas Thiemann, Hanno Sahlmann, Jesper Grimstrup, Raimar Wulkenhaar, their co-workers, and several others.

It took place the week of 7-13 February at Oberwolfach. Was organized by Marcolli together with Christian Fleischhack and Ryzard Nest.

Jesper Grimstrup has visited the Beyond forum at PF--I remember exchanging messages with him. He and co-author Johannes Aastrup were among the first researchers to try combining LQG with Noncommutative Geometry.

Here's the program of the February workshop, with expanded abstracts of the various papers that were delivered:
http://www.mfo.de/programme/schedule/2010/06b/OWR_2010_09.pdf

Noncommutative Geometry and Loop Quantum Gravity: Loops, Algebras and Spectral Triples

 

[MTd2]

I thought you'd open a thread for at least 1 of the papers by Rovelli yesterday. Don't you think they were groundbreaking?

 

[marcus]

Rovelli's program is already going gangbusters with a lot of momentum. Let's keep an eye on some of the smaller, newer efforts like putting NCG into the picture with Loop Quantum Gravity.

One important outcome of this workshop is the paper that just appeared by Marcolli et al

http://arxiv.org/abs/1005.1057
Spin Foams and Noncommutative Geometry
Domenic Denicola (Caltech), Matilde Marcolli (Caltech), Ahmad Zainy al-Yasry (ICTP)
48 pages, 30 figures
(Submitted on 6 May 2010)
"We extend the formalism of embedded spin networks and spin foams to include topological data that encode the underlying three-manifold or four-manifold as a branched cover. These data are expressed as monodromies, in a way similar to the encoding of the gravitational field via holonomies. We then describe convolution algebras of spin networks and spin foams, based on the different ways in which the same topology can be realized as a branched covering via covering moves, and on possible composition operations on spin foams. We illustrate the case of the groupoid algebra of the equivalence relation determined by covering moves and a 2-semigroupoid algebra arising from a 2-category of spin foams with composition operations corresponding to a fibered product of the branched coverings and the gluing of cobordisms. The spin foam amplitudes then give rise to dynamical flows on these algebras, and the existence of low temperature equilibrium states of Gibbs form is related to questions on the existence of topological invariants of embedded graphs and embedded two-complexes with given properties. We end by sketching a possible approach to combining the spin network and spin foam formalism with matter within the framework of spectral triples in noncommutative geometry."

 

[marcus]

Besides, MTd2, look at that knowing smile:
http://www.its.caltech.edu/~matilde/

 

[MTd2]

Interesting that paper. I guess my friend Torsten will like it. It seems a paper he would like to work on, since she discuss a bit about the relation between diffeomorphism and topology. And one of her students posted a paper on one of Torsten's exotic smoothness. She cites him on [23]

BTW, I still think you should open that thread.