bio  website  sci.ccny.cuny.edu/~benjamin 

location  New York City  
age  42  
visits  member for  3 years, 6 months 
seen  9 hours ago  
stats  profile views  7,430 
I am an algebraist interested in a broad range of areas. I've worked on semigroups, geometric group theory, algebraic combinatorics, representation theory, selfsimilar groups (aka automaton groups), profinite groups and random walks on semigroups and groups. I've been particularly interested in interactions between these areas and Computer Science and am fond of algorithmic questions. I've also dabbled with operator algebras associated to etale groupoids and inverse semigroups. Currently, I am interested in applications of finite semigroup theory to finite state Markov chains.
My blog is http://bensteinberg.wordpress.com/author/bsteinbg/
1d

comment 
Is a free group a product of f.g subgroups of infinite index?
Ok. Fair enough. 
1d

comment 
Is a free group a product of f.g subgroups of infinite index?
Why not use the slightly easier version of this argument suggested in my comment to the question? By Marshall hall you can assume that one of the subgroups H is a free factor. The covering space or Schreier graph associated to K has a finite core, the stallings graph. Outside this core you have infinitely many orbits of H so infinitely many double cosets. Both being free factors is not needed. 
2d

comment 
Is a free group a product of f.g subgroups of infinite index?
Can you not use Marshall Hall's theorem to reduce to the case where one of the subgroups is a free factor? If one of the subgroups is a proper free factor then you can use the finiteness of the Stallings graph of the other to show you can't reach every vertex in the Schreier graph using generators from the first factor. 
Dec 15 
comment 
Is there a left orderable profinite group?
The partial order is a set of ordered pairs. If this is set is closed in the product topology the ordering will be trivial. 
Dec 15 
comment 
Is there a left orderable profinite group?
If the order is closed in the topology on the direct product the answer is no by reduction to the finite case I believe. 
Dec 8 
comment 
Counting path generating sentences in a specific formal language
I find the question hard to parse. Do you want the generating function for derivations of words using the grammar or the generating function for the language? 
Dec 8 
revised 
Counting path generating sentences in a specific formal language
added 2 characters in body 
Dec 5 
comment 
Is there a nontrivial profinite word which is trivial in any group with at most d generators?
The one in the title would seem to indicate you just need to separate a word from 1 in a not necessarily onto homomorphism to a 2generated finite group, which you can do since symmetric groups are 2generated. 
Dec 5 
comment 
Is there a nontrivial profinite word which is trivial in any group with at most d generators?
The question in the title is different an easier than the one in the body. @HWJR seems to be answering the one in the title. 
Dec 3 
revised 
Dehn algorithm and normal forms in small cancellation groups
added 11 characters in body 
Dec 3 
comment 
Dehn algorithm and normal forms in small cancellation groups
Derek, will fix it. 
Dec 3 
comment 
Dehn algorithm and normal forms in small cancellation groups
Yes, Derek. That one. 
Dec 2 
comment 
Dehn algorithm and normal forms in small cancellation groups
is this the paper where they look at which groups have a finite confluent rewriting system that turns any word into a geodesic? They had a conjecture that I started to look at years ago with A. Weiss and this is why I remembered your paper with Gilman and Rees. 
Dec 2 
revised 
Dehn algorithm and normal forms in small cancellation groups
added 407 characters in body 
Dec 2 
comment 
Dehn algorithm and normal forms in small cancellation groups
What is meant by deterministic variation is ambiguous but applying a finite set of length reducing rules is excluded by the above paper. 
Dec 2 
answered  Dehn algorithm and normal forms in small cancellation groups 
Nov 27 
awarded  Nice Answer 
Nov 20 
revised 
Systems of equations in Boolean Algebra
added 916 characters in body 
Nov 20 
comment 
Systems of equations in Boolean Algebra
Some of this is discussed in Chapter 9 of my book with John Rhodes, The qtheory of finite semigroups. Either the result you want or its dual might even be there or in my paper with Izhakian and Rhodes on representations of monoids over semirings. I don't have references in front of me. I can try to write something more when I have a better computer than a smartphone 
Nov 20 
answered  Systems of equations in Boolean Algebra 