Hebrew University
 
Amitsur Algebra Seminar
---------------------------------
 
Time: Thursday, Dec 29, 12:00-13:15
 
Place: math 209
 
Speaker: Doron Puder (HUJI)
 
Title:  Primitive Words in Free Groups (Cont.)
 
Abstract:
 
This is a third talk in a series (following the 8.12 Colloquium talk
and 15.12 Amitsur talk). We shall try to convey the remaining ideas of
the proof of the results mentioned below.
 
We consider two properties of words in F_k, the free group on k
generators. A word w is called primitive if it belongs to a basis
(i.e. a free generating
set) of F_k. It is called measure preserving if for every finite group
G, all elements of G are
obtained by the word map $w : G^k \to G$ the same number of times.
 It is an easy observation that a primitive word is measure
preserving. Several mathematicians, most notably from Jerusalem, have
conjectured that the converse is also true. After proving the
special case of F_2, we manage to prove the conjecture in full in a
recent joint work with O. Parzanchevski. As an immediate corollary, we
prove another
conjecture and show that the set of primitive words in F_k is closed
in the profinite topology.
 
Different tools are used in the proof, including Stallings core
graphs, random coverings of graphs, Mobius inversions and algebraic
extensions of free groups.
The proof also involves a new algorithm to detect primitive words and a new
categorization of free words.
 
You are cordially invited!
 
 <http://math.huji.ac.il/amitsur.html>
 
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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Gili Schul   <gili.schul@mail.huji.ac.il>