School of Mathematics & Physics, University of Lincoln
On Thursday the 3rd of February, 2022, Alex Lubotzky (Weizmann Institute and Hebrew University, Israel) will give an online talk “Stability and testability of permutations’ equations” at 16:00 Novosibirsk time (9:00 London time).
Abstract: Let A and B be two permutations in Sym(n) which “almost commute” — are they a small deformation of permutations that truly commute? More generally, if R is a system of word-equations in variables X=(x_1,….,x_d) and A=(A_1,…., A_d) permutations which are nearly solution; are they near true solutions? It turns out that the answer to this question depends only on the group presented by the generators X and relations R. This leads to the notions of “stable groups” and “testable groups”. We will present a few results and methods which were developed in recent years to check whether a group is stabletestable. We will also describe the connection of this subject with property testing in…
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