15,998 reputation
23797
bio website sci.ccny.cuny.edu/~benjamin
location New York City
age 42
visits member for 4 years
seen 1 hour 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/


Jun
25
comment Independence of inverse system to define continuous cohomology for profinite groups
Presumably this is what the op means.
Jun
25
comment Independence of inverse system to define continuous cohomology for profinite groups
This definition is usually shown equivalent to the various other ones in most books like Wilson's book or Ribes and Zalesski
Jun
24
awarded  Good Answer
Jun
23
comment Next steps on formal proof of classification of finite simple groups
This seems the ideal project for computerized proofs. It is a highly cited result that many people take as a black box and which one gets the impressions has skeptics. I am not sure that a computer proof will help the true skeptics but probably some people will sleep slightly better at night knowing that there are both human and computer proofs (I just hope a computer proof wouldn't dissuade people from continuing the revision of the human proof).
Jun
22
awarded  Yearling
Jun
21
awarded  Nice Answer
Jun
19
comment pro-p dense subgroup in the free group
@YCor, this is surely what the op meant
Jun
19
revised pro-p dense subgroup in the free group
added 8 characters in body
Jun
18
awarded  Nice Question
Jun
7
comment Why is every variety of bands determined by a single identity?
@Gerhard, yes I meant by a single finite semigroup
Jun
6
comment Why is every variety of bands determined by a single identity?
No it is just to help fill in the picture. It is not true that every proper subvariety of a locally finite variety is finitely generated.
Jun
6
comment Why is every variety of bands determined by a single identity?
You might look at Gerhard, J. A.; Petrich, Mario Varieties of bands revisited. Proc. London Math. Soc. (3) 58 (1989), no. 2, 323–350 which claims to give a more conceptual approach to the lattice of band varieties.
Jun
6
comment Why is every variety of bands determined by a single identity?
If you go to quasivarieties the situation is different. The result of adjoining an identity to a 2-element left zero semigroup has no finite basis of quasi-identities.
Jun
6
comment Why is every variety of bands determined by a single identity?
Each proper subvariety of bands is generated by a single semigroup.
Jun
6
comment Why is every variety of bands determined by a single identity?
@EWHLee may know.
Jun
6
comment Why is every variety of bands determined by a single identity?
Bands are a bit miraculous. I never understood this myself.
Jun
6
comment Why is every variety of bands determined by a single identity?
The variety generated by any finite group is defined by a single identity. This is a deep theorem of Powell - Oates.
Jun
4
comment Show that representative functions on a profinite group factors.
More or less right. The image of G is compact because the images of compact sets are compact.
Jun
4
comment Show that representative functions on a profinite group factors.
Or put an answer on the mse version
Jun
4
comment Show that representative functions on a profinite group factors.
It is better to do this on mathstack exchange. MO is for research. It is better not to put an answer.