Here is an update (from a noncommutative geometry point of view) of the talks at the conference Frontiers of Fundamental Physics. The conference started off with a great welcome reception at the Fort Ganteaume, enjoying a great view on the fireworks for the 14th of July.
On Monday morning there was a nice overview on the status of HEP after LHC run 1 by Paraskesas Sphicas, were especially the experimental finding of spin 0 for the Higgs boson is interesting for NCG and applications where it naturally appears as a scalar boson.
In one of the so-called `parallel plenary’ sessions Pierre Bieliavsky gave an overview of deformation quantization using the deformation of a matrix algebra as an interesting 0-dimensional toy model.
There were two interesting contributions on causal structures in noncommutative geometry, addressing some of the first questions on the way towards a Lorentzian version of spectral triples. Fabien Besnard introduces so-called \(I^*\)-algebras that translates to the \(C^*\)-algebraic level the causal structure on the state space of that \(C^*\)-algebra. A reference is
Mickal Eckstein presented some of his recent work with Nicolas Franco on Lorentzian spectral triples, arriving at a different notion of causality in the context of spectral triples. Some of the examples he discussed were two-sheeted spacetime for which he derived a causal relation between the two sheets when the distance in the continuous direction was larger than the distance in the discrete direction. The corresponding paper is in preparation.