Noncommutative Geometry Seminar

I will discuss the vacuum structure of the standard model coupled to gravity with two
spatial dimensions compactified on a two-torus or a two-sphere, as well as the case
of all spatial dimensions compactified on a three-torus. I will show that for the two-dimensional
compactification on a torus there exists a new standard model vacuum stabilized by
Casimir energies of standard model particles for a large range of experimentally allowed
neutrino masses. I will also describe how finite temperature effects modify this picture and
discuss the possibility of transitions between the four-dimensional universe and the
compactified spacetimes.