Comments on: The structure of approximate groups

By: Carry propagation-free number systems and a kind of approximate groups (I) | chorasimilarity

Sun, 21 Apr 2013 08:13:03 +0000

[...] (that’s what qualifies as a kind of an approximate group). [...]

By: Small doubling in groups « What’s new

Small doubling in groups « What’s new — Fri, 01 Feb 2013 18:19:52 +0000

[...] have Lie structure; this connection was first observed and exploited by Hrushovski, and then used by Breuillard, Green, and myself to obtain the analogue of Freiman’s theorem for an arbitrary nonabelian [...]

By: Approximate groupoids again « chorasimilarity

Approximate groupoids again « chorasimilarity — Fri, 04 Jan 2013 15:05:54 +0000

[...] Here is the path I would like to pursue further. The notion of approximate groupoid (see here for the definition) is not complete, because it is flattened, i.e. the set of arrows should be seen as a set of variables. What I think is that the correct notion of approximate groupoid is a polynomial functor over groupoids (precisely a specific family of such functors). The category Grpd is cartesian closed, so it has an associated model of (typed) lambda calculus. By using this observation I could apply emergent algebra techniques (under the form of my graphic lambda calculus, which was developed with — and partially funded by – this application in mind) to approximate groupoids and hope to obtain streamlined proofs of Breuillard-Green-Tao type results. [...]

By: A geometric viewpoint on computation? | chorasimilarity

A geometric viewpoint on computation? | chorasimilarity — Sun, 20 May 2012 11:13:55 +0000

[...] the profound resemblance between geometrical results of Gromov on groups with polynomial growth and combinatorial results of Breuillard, Gree, Tao on approximate groups? In both cases a nilpotent structure emerges from considering larger and larger scales. The word [...]

By: mac özeti

mac özeti — Mon, 09 Apr 2012 11:57:39 +0000

Thank you for the answer, very interesting! A Gleason metric is a CC metric if and only if the nilpotent group is abelian, because of the commutator estimate.

By: 254A, addendum: Some notes on nilprogressions « What’s new

254A, addendum: Some notes on nilprogressions « What’s new — Sun, 18 Mar 2012 05:12:38 +0000

[...] groups, and use it to prove the above proposition, which turns out to be a bit tricky. (In my paper with Breuillard and Green, we avoid the need for this proposition by restricting attention to a special type of [...]

By: A nilpotent Freiman dimension lemma | t1u

A nilpotent Freiman dimension lemma | t1u — Thu, 22 Dec 2011 00:50:03 +0000

[...] remark that our previous paper established a similar result, in which the dimension bound was improved to , but at the cost of [...]

By: A nilpotent Freiman dimension lemma « What’s new

A nilpotent Freiman dimension lemma « What’s new — Thu, 22 Dec 2011 00:24:08 +0000

[...] remark that our previous paper established a similar result, in which the dimension bound was improved to , but at the cost of [...]

By: Approximate algebraic structures, emergent algebras | chorasimilarity

Approximate algebraic structures, emergent algebras | chorasimilarity — Fri, 09 Dec 2011 15:52:47 +0000

[...] algebra can also be seen as an approximate algebraic structure! But in a different sense than approximate groups. The operations themselves are approximately associative, for [...]

By: 254A, Notes 8: The microstructure of approximate groups « What’s new

254A, Notes 8: The microstructure of approximate groups « What’s new — Thu, 01 Dec 2011 15:58:18 +0000

[...] must be replaced by the local version of this theorem, due to Goldbring); details can be found in this recent paper of Emmanuel Breuillard, Ben Green, and myself, but will only be sketched [...]