Dr. Alessia Kogoj

Department of Mathematics, University of Bologna

**Title:** Subelliptic Liouville theorems

**Abstract: **Some Liouville-type theorems are presented, related to evolution equations and to their stationary counterpart. The equations we are dealing with are homogeneous with respect to a group of dilations and, in some cases, left translations invariant on a Lie group structure. In all these cases the operators have smooth coefficients and are hypoelliptic at least in a neighborhood of the origin. We also present a “polynomial” Liouville-type theorem for X-elliptic operators with nonsmooth coefficients, by extending to this new setting a celebrated result by Colding and Minicozzi related to the Laplace-Beltrami operator on Riemannian manifolds.</td>