Mathematics

Connes' notion of non-commutative geometry (NCG) generalizes Riemannian geometry and yields a striking reinterepretation of the standard model of particle physics, coupled to Einstein gravity.  In my talk I suggest a simple reformulation of Connes' approach which resolves a long-standing problem plaguing the NCG construction of the standard model, by precisely eliminating from the action the collection of 7 unwanted terms that previously had to be removed by an extra, non-geometric, assumption. I will also show how this same reformulation yields a new perspective on the symmetries of a given NCG, which offers a new solution to the discrepancy between the observed Higgs mass and the NCG prediction.