Comments on: Mixing for progressions in non-abelian groups
https://terrytao.wordpress.com/2012/12/11/mixing-for-progressions-in-non-abelian-groups/
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence TaoSat, 05 Sep 2015 07:05:09 +0000hourly1http://wordpress.com/By: Terence Tao
https://terrytao.wordpress.com/2012/12/11/mixing-for-progressions-in-non-abelian-groups/#comment-204683
Thu, 13 Dec 2012 16:01:32 +0000http://terrytao.wordpress.com/?p=6395#comment-204683That’s a great question, and resolving it in a sufficiently “robust” fashion would likely lead to the removal of the hyperbolicity restriction in my length four progression results. I did try my hand at this for a while, but could not algebraically simplify the four-term version of (2) by the techniques of changing variable and cancelling (which, roughly speaking, is to the 100% world as Cauchy-Schwarz type methods are to the 1% world). But perhaps another approach is possible (though if the approach is too “global” in nature, it may be restricted to the 100% or 99% worlds, and not to the 1% world which is the world in which the actual problem is set).
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https://terrytao.wordpress.com/2012/12/11/mixing-for-progressions-in-non-abelian-groups/#comment-204617
Thu, 13 Dec 2012 14:34:51 +0000http://terrytao.wordpress.com/?p=6395#comment-204617Is it the situation that in the case of the four term progression for which a group element g is non-hyperbolic, that there might probably be a constraint such as (2) above for all x?
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