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 stable\testable. We will also describe the connection of this subject with property testing in computer science, with the long-standing problem of whether every group is sofic and with IRS’s ( =invariant random subgroups).
A number of open questions will be presented.
Chair of the session: Mikhail Belolipetsky
The link to the Zoom meeting: https://us02web.zoom.us/j/3167567840?pwd=aExXZmUxVmE5blYxYTVRMHhrakxuQT09 (ID 316 756 7840, Password gD11t2).
See the program updates at http://mca.nsu.ru/kourovkaforum/.
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