Motivic Dreams

To show that all L-functions associated to Shimura varieties - thus to any motive defined by a Shimura variety - can be expressed in terms of automorphic L-functions of is weaker, even very much weaker, than to show that all motivic L-functions are equal to such L-functions.  Moreover, although the stronger statement is expected to be valid, there is, so far as I know, no very compelling reason to expect that all motivic L-functions will be attached to Shimura varieties.  - R. Langlands

The Father of Motives

With the passing of Alexander Grothendieck, there is much discussion comparing him to Einstein in the mathematics world.  I think it would be more fitting to compare him to Riemann, whose differential geometry made General Relativity possible.  Of course, this is meant in a future tense as it is extremely likely Grothendieck's Motives will play a central role in the nonperturbative completion of M-theory.

Matrix theory Revisited

Progress has been made on matrix descriptions of the lattices for E10, E11 and K27.  It's a great time to return to Chern-Simons like matrix models with cubic actions.

M-theory: The Final Frontier

After a week at UCLA and Caltech, it appears M may very well stand for Motives.

Unified Theory of Mathematics

 

What do the Langland's program and Monstrous Moonshine have in common?  The answer lies in M-theory.  Stay tuned.

The Higgs Vacuum is Unstable

 arXiv:1404.4709 [hep-ph]
Abstract:

So far, the experiments at the Large Hadron Collider (LHC) have shown no sign of new physics beyond the Standard Model. Assuming the Standard Model is correct at presently available energies, we can accurately extrapolate the theory to higher energies in order to verify its validity. Here we report the results of new high precision calculations which show that absolute stability of the Higgs vacuum state is now excluded. Combining these new results with the recent observation of primordial gravitational waves by the BICEP Collaboration, we find that the Higgs vacuum state would have quickly decayed during cosmic inflation, leading to a catastrophic collapse of the universe into a black hole. Thus, we are driven to the conclusion that there must be some new physics beyond the Standard Model at energies below the instability scale ΛI∼109 GeV, which is responsible for the stabilisation of the Higgs vacuum.