13,851 reputation
23285
bio website sci.ccny.cuny.edu/~benjamin
location New York City
age 41
visits member for 3 years, 2 months
seen 2 days 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/


Aug
1
comment Can a closure make the index finite?
@HJRW I wrote a similar but more complicated example at the same time.
Aug
1
revised Can a closure make the index finite?
added 6 characters in body
Aug
1
revised Can a closure make the index finite?
added 6 characters in body
Aug
1
comment Can a closure make the index finite?
Which Karrass-Solitar Thm? They have many.
Aug
1
awarded  Favorite Question
Aug
1
answered Can a closure make the index finite?
Jul
30
comment Is every compact monothetic group metrizable?
Basically monothetic compact groups correspond to subgroups of $S^1_\delta$ and the metrizable ones correspond to countable subgroups.
Jul
30
comment Is every compact monothetic group metrizable?
Your group G is metrizable iff $\widehat{G}$ is countable.
Jul
30
comment How much of homotopy theory can be done using only finite topological spaces?
Do you know the book Barmak, Jonathan, Algebraic Topology of Finite Topological Spaces and Applications, Springer 2011?.
Jul
30
comment Is every compact monothetic group metrizable?
The dual of a countable group is metrizable because it embeds in a countable direct product of $S^1$ and a countable product of metric spaces is metric.
Jul
30
comment Is every compact monothetic group metrizable?
Did you try using Pontryagin duality?
Jul
25
awarded  Nice Answer
Jul
24
comment Examples of famous 'workhorse' theorems
Related mathoverflow.net/questions/99506/blackbox-theorems
Jul
18
answered a question about semigroups
Jul
18
comment a question about semigroups
Are you asking which semigroups have the property that the intersection of any two ideals is there product?
Jul
18
comment Reference for subsemigroups of $\mathbb{N}^n$
@LeeMosher, thanks.
Jul
14
answered Which algebraic theories have the property that $\mid$ is antisymmetric for all free algebras?
Jul
14
comment Which algebraic theories have the property that $\mid$ is antisymmetric for all free algebras?
In semigroup theory this preorder is called the $\mathcal J$-order. A semigroup is called $\mathcal J$-trivial if it is a partial order. There are a number of natural varieties of semigroups and monoids where all free algebras are J-trivial. Note J-triviality is given by finitely many quasiidentities. For finitary universal algebras you may need infinitely many.
Jul
14
comment Which algebraic theories have the property that $\mid$ is antisymmetric for all free algebras?
But the theory is the theory of monoids and semigroups. In your question you only ask about the relation on free objects.
Jul
14
comment Which algebraic theories have the property that $\mid$ is antisymmetric for all free algebras?
This relation is antisymmetric for monoids and semigroups without abelian and for many natural subvarieties.