Approximate actions and Ulam stability

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• Oren Becker (University of Cambridge)
• Friday 08 November 2019, 13:45-14:45
• CMS, MR13.

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Given two permutations A and B in Sym(n) such that AB and BA are almost equal, are there A’ and B’ in Sym(n) such that A is close to A’, B is close to B’, and A’B’=B’A’? Arzhantseva and Paunescu formalized this question and gave an affirmative answer: “Nearly commuting permutations are near commuting permutations”. Equivalently, approximate actions of the group Z² on finite sets are close to genuine actions, i.e., Z² is stable (in permutations). I will discuss the more general problem: Which finitely generated groups are stable?

This will bring into the picture notions such as Property (T), amenability, invariant random subgroups, sofic groups and property testing.

The talk is based on joint works with Alex Lubotzky, Andreas Thom and Jonathan Mosheiff.

This talk is part of the Geometric Group Theory (GGT) Seminar series.

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