14,573 reputation
23287
bio website sci.ccny.cuny.edu/~benjamin
location New York City
age 42
visits member for 3 years, 6 months
seen 9 hours ago

I am an algebraist interested in a broad range of areas. I've worked on semigroups, geometric group theory, algebraic combinatorics, representation theory, self-similar 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 2-generated finite group, which you can do since symmetric groups are 2-generated.
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 q-theory 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