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Tuesday, 30 June 2026 - 10:00 to 11:30 <br />
Place: IM, konÃrna
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Speaker: Yonatan Gutman, Institute of Mathematics of the Polish Academy of Sciences<br />
Title: Finite-to-one extensions into cubical shifts
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Abstract <br />
<p>We prove that any dynamical system $(X,T)$ that admits the marker property and has mean dimension strictly less than $d$ admits a continuous, finite-to-one equivariant map into $(([0,1]^d)^\mathbb{Z},\operatorname{shift})$. Moreover, in the above situation a generic continuous equivariant map from $X$ to $([0,1]^d)^\mathbb{Z}$ is finite-to-one. In particular when $\operatorname{mdim}(X,T) < \frac{1}{2}d$, we show that such a generic continuous equivariant map is an embedding and this strengthens the optimal embedding theorem of Gutman, Qiao, and Tsukamoto (2019), for $\mathbb{Z}$-actions.</p><p>Unlike earlier works, our proof relies on classical topological techniques originating in the work of Ostrand (1965), Kolmogorov (1957), and Arnold (1957).</p><p>Based on a joint work with Michael Levin and Tom Meyerovitch.</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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