Speaker: Doron Puder (Jerusalem)
Title: Growth of Primitive Elements in Free Groups

Abstract:
In the free group F_k an element is said to be primitive if
it belongs to a free generating set. 
But how do "most" primitive elements look like? 
We give a somewhat surprising result: 
It turns out that most primitives are words which are "obviously" primitive,
namely, words which, up to conjugation, contain one of the letters exactly
once.
 
This also solves a question from the list
`Open problems in combinatorial group theory'
[Baumslag-Myasnikov-Shpilrain 02']. 
Let p_{k,N} be the number of primitive words of length N in F_k.
We show that for k>2 the exponential growth rate of p_{k,N} is 2k-3. 
Our proof also works for giving the exact growth rate of the larger class
of elements belonging to a proper free factor.
 
Joint with Conan Wu