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
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,
Seminar webpage:
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <> 
Announcement from: Ron Peled   <>