This Mini-Lecture Series will consist of three talks of 50 minutes each.
Abstract: In the series of three talks I will discuss unipotent dynamics in a non-linear world. In the first talk, I will review some classical results in linear groups of rank one; the main example being - the action of the unipotent group U < SL(2,R) on the homogeneous space SL(2,R)/SL(2,Z). The second talk will focus on introducing nonlinear analogues of all the players. The role of SL(2,R) will be played by the group of tree automorphisms. I will discuss lattices in it and prove orbit classification. In the third talk, I will explain measure classification and some equidistribution results in the non-linear setting. This is joint work with C.Ciobotaru and C.Sert.