27.05.2021 – Seminarium Katedry Geometrii – dr hab. Yonatan Gutman, prof. IM PAN

Uprzejmie informujemy, że na seminarium Katedry Geometrii w czwartek, 27 maja 2021, godz. 10:15
wykład wygłosi dr hab. Yonatan Gutman z Instytutu Matematycznego PAN.

Title: Optimal embedding of topological dynamical systems.
Abstract: Given a metrizable space $X$ of dimension $d$, it is a classical fact that the minimal $n$ which guarantees that $X$ may be embedded topologically in $[0,1]^n$, is $n=2d+1$. In the category of dynamical systems, one considers the analogous problem of under what conditions one can guarantee that a topological dynamical system $(X,T)$  embeds in $([0,1]^n)^\mathbb{Z}$ under the shift action.

We will review the history of the embedding problem starting from the famous Bebutov-Kakutani embedding theorem (1968) through Jaworski’s theorem (1974) and Takens’ delay embedding theorem (1981) culminating in the rapid developments in the last 20 years starting with Gromov’s introduction of the invariant of mean dimension (1999) and the breakthrough results of  Lindenstrauss and Weiss (2000).  We will indicate the current state of the art and present some key theorems.  In particular, we will present our joint result with Tsukamoto concerning the optimal embedding of minimal systems (2020) whose proof involves a surprising connection to signal analysis.

Serdecznie zapraszamy do udziału w seminarium,

Andrzej Biś

Link do seminarium w aplikacji MS Teams:

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