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Tuesday, 1 April 2025 - 10:00 to 11:30 <br />
Place: IM, konÃrna
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Speaker: Michal Doucha, IM CAS<br />
Title: Generic actions of free groups on the Cantor space
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Abstract <br />
<p>M. Hochman proved that the universal odometer is a generic minimal homeomorphism on the Cantor space (also a generic topologically transitive homeomorphism). The aim of my talk is to generalize these results for tuples of homeomorphisms, i.e. to consider actions of free groups instead of actions of the integers.</p><p> I will show how the generalization naturally splits into two directions: There is a generic minimal action of a given free group on the Cantor space as well as a generic probability measure preserving minimal action of that free group. While for the integers these two actions coincide, for non-abelian free groups they are different. On the other hand, there is no generic topologically transitive action of a non-abelian free group.</p><p> This is a part of joint work in progress with Julien Melleray and Todor Tsankov.</p>
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For more information see the seminar web page at <br />
https://www.math.cas.cz/index.php/events/seminar/6
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Set Theory and Analysis mailing list <br />
settfa@math.cas.cz <br />
https://list.math.cas.cz/listinfo/settfa@math.cas.cz
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