Speaker: **Oleksii Rudenko** (Institute of Mathematics of NAS of Ukraine)

Topic: **The intersection of small balls with a hypersurface in Carnot group and Brownian motion in Carnot group**

Abstract. *We consider a Carnot group and a smooth hypersurface in it. Taking a ball w.r.t. natural distance in Carnot group we study its surface measure w.r.t. the given hypersurface. The estimates of such measure when the radius of the ball is small will be presented. We will also discuss how such estimates are connected to the properties of the corresponding Brownian motion on Carnot group.*