Dennis The, UiT The Arctic University of Norway
"A Cartan-theoretic classification of multiply-transitive (2,3,5)-distributions"
Generic rank 2 distributions on 5-manifolds, i.e. (2,3,5)-distributions, are interesting geometric structures arising in the study of non-holonomic kinematical systems (e.g. two 2-spheres rolling on each other without twisting or slipping), underdetermined ODE of Monge type, conformal 5-manifolds with special holonomy, etc. The origins of their study date to Élie Cartan's "5-variables" paper of 1910, where he gave a tour-de-force application of his method of equivalence. In particular, he obtained a canonical coframing, discovered a fundamental (tensorial) curvature quantity (the Cartan quartic), and gave a (almost complete) local classification of structures that are multiply-transitive, i.e. (locally) homogeneous with isotropy of positive dimension. In my talk, I'll revisit this homogeneous classification and present it from a modern Cartan-geometric perspective.
Zoom link: https://zoom.us/j/93859138328; Passcode: 436044