Dept Math & Stat UiT, Forskningsparken B459
12 Jun 2025 Wed
14:15-16:00
Dennis The (UiT)
"Symmetries of (2,3,5)-distributions and associated Legendrian cone structures"
The study of (2,3,5)-distributions is a classical subject, originating with Elie Cartan's tour-de-force study in 1910. Nowadays, it is a prototypical example of a parabolic geometry, and this perspective is key for identifying salient geometric features. In this talk, I'll discuss recent work (joint with Jun-Muk Hwang) approaching their study from the point of view of a certain canonical double fibration, and the resulting geometric structures on the so-called space of abnormal extremals. This offers new insights on this classical topic, which I'll describe. In particular, for the (2,3,5) "rolling distribution" of two 2-spheres rolling on each other without twisting or slipping, this perspective yields a nice geometric interpretation of exceptionality of the 3:1 ratio of radii (known to yield G2 symmetry).