New Alain Connes Paper: Read Now

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A new paper by Alain Connes has been released, generating excitement for its potential contributions to the field. It proposes a generalization of the renormalization group that functions as a true group, which aligns with the aspirations of notable mathematicians like Cartier and Grothendieck. The paper also addresses dimensional regularization and minimal subtraction, providing clarity that many in the field have sought. Readers are finding the explanations accessible, even when delving into more complex topics like divergent graphs. Overall, the paper is seen as a valuable resource for advancing understanding in noncommutative geometry and related areas.
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It just keeps coming, doesn't it! Great!
 
It seems the new recruitment, Matilde Marcolli, is very diligent!
 
Do I read this correctly, they have a generalization of the renormalization "group"? One that really is a group?
 
selfAdjoint said:
Do I read this correctly, they have a generalization of the renormalization "group"? One that really is a group?

The dream of Cartier and the Grothendieck's of this world! Yep - the cosmic Galois group. Of course now we just need to sort out the noncommutative case...
 
I am reading the paper now. The beginning, where they go over the dimesnional regularization and minimal subtraction is just what I have needed for a long time. I am a receptive-minded person, which means I have to have a minimal structure for data in my head before I can really take it in. This ultraclear summary presents what I have needed to get behind the calculational facade of dimensional regularization. Am now onto the divergent graph material, which is unfamiliar to me but still very clear. I am so glad this paper exists!
 
"Supernovae evidence for foundational change to cosmological models" https://arxiv.org/pdf/2412.15143 The paper claims: We compare the standard homogeneous cosmological model, i.e., spatially flat ΛCDM, and the timescape cosmology which invokes backreaction of inhomogeneities. Timescape, while statistically homogeneous and isotropic, departs from average Friedmann-Lemaître-Robertson-Walker evolution, and replaces dark energy by kinetic gravitational energy and its gradients, in explaining...

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