Kourovka Forum: talk by Alex Lubotzky

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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