Event № 125
A geometric transition is a continuous path of geometries which abruptly changes type in the limit. We explore geometric transitions of the positive diagonal Cartan subgroup in SL(n,R). For n = 3, it turns out the diagonal Cartan subgroup has precisely 5 limits, and for n = 4, there are 15 limits, which give rise to generalized cusps on convex projective 3-manifolds. When n ≥ 7, there is a continuum of non conjugate limits of the Cartan subgroup, distinguished by projective invariants. To prove these results, we use some new techniques of working over the hyperreal numbers.
This first talk will focus on n=3 and hyperreal techniques. It should be very accessible.