Date:	Thu, April 9, 2015
Time:	15:45
Place:	Seminar Room (120), Research I

Abstract: A celebrated theorem of Milnor and Wolf states that a finitely generated solvable group is either of polynomial or exponential (word) growth. This result was subsequently strengthened by Rosenblatt, who showed that there is indeed an alternative: a given solvable group has either polynomial growth and is, hence, virtually nilpotent, or, it contains a free semigroup on two generators, witnessing the exponential growth.
In this talk, we will state and sketch the proof of various generalizations of Rosenblatt's theorem. For instance, we will show that if \(G\) is a finitely generated linear solvable group of exponential growth with a connected Zariski closure, then \(G\) contains a free semigroup, which is Zariski dense in \(G\). We will also study situations in which a random sub-semigroup of a given solvable group is free, with high probability. The talk is elementary and all the required definitions will be provided.