Tel Aviv University Dear all, This week at the Horowitz seminar on Probability, Ergodic Theory and Dynamical Systems at Tel Aviv University we are happy to have: Speaker: Doron Puder, The Hebrew University of Jerusalem Title: Uniform Words are Primitive Date: Monday, November 28 Time: 14:30 Place: Schreiber 309 Abstract: Let a,b,c,... in S_n be random permutations on n elements, chosen at uniform distribution. What is the distribution of the permutation obtained by a fixed word in the letters a,b,c,..., such as ab,a^2, a^2bc^2b, or aba^(-2)b^(-1)? More concretely, do these new random permutations have uniform distribution? In general, a free word w in the free group F_k is called uniform if for every finite group G, the word map $w: G^k \to G$ induces uniform distribution on G (given uniform distribution on G^k). So which words are uniform? This question is strongly connected to the notion of primitive words in the free group F_k. The word w is called primitive if it belongs to some basis, i.e. a free generating set. It is an easy observation that a primitive word is uniform. It was conjectured that the converse is also true. We prove it for F_2, and in a recent joint work with O. Parzanchevski, we manage to prove the conjecture in full. A key ingredient of the proofs is a new algorithm to detect primitive elements. Best regards, Ron Seminar webpage: <http://www.math.tau.ac.il/~peledron/Horowitz_seminar/Horowitz_seminar.html> --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Ron Peled <peledron@gmail.com>