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start [2024/04/18 13:32] – 139.124.146.3start [2024/04/30 22:51] – 139.124.146.3
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-**April 30 2024: [[https://www.math.uni-bielefeld.de/baake/|Michael Baake]]** //Hats, CAPs and Spectres//+**May 14 2024: [[https://dblp.org/pid/10/10715.html|Josef Rukavicka]]** //Restivo Salemi property for $\alpha$-power free languages with $\alpha \geq 5$ and $k \geq 3$ letters//
  
-The recently discovered Hat is an aperiodic +In 2009, Shur published the following conjecture: Let $L$ be a power-free language and let $e(L)\subseteq L$ be the set of words of $L$ that can be extended to a bi-infinite word respecting the given power-freeness. If $u,v \in e(L)$ then $uwv \in e(L)$ for some word $w$. Let $L_{k,\alpha}$ denote an $\alpha$-power free language over an alphabet with $k$ letters, where $\alpha$ is a positive rational number and $k$ is positive integer. We prove the conjecture for the languages $L_{k,\alpha}$, where $\alpha\geq 5$ and $k \geq 3$.
-monotile for the Euclidean plane, which needs a reflected +
-version for this property. The Spectre does not have this +
-(tiny) deficiency. We discuss the topological and dynamical +
-properties of the Hat tiling, how the CAP relates to it, and +
-what the long-range order of both tilings is. Finally, we +
-briefly describe the analogous structure for the Spectre tiling.+
  
- +https://arxiv.org/abs/2312.10061
-**May 14 2024: [[https://dblp.org/pid/10/10715.html|Josef Rukavicka]]**+
  
 **May 28 2024: [[https://www.lirmm.fr/~ochem/|Pascal Ochem]]** **May 28 2024: [[https://www.lirmm.fr/~ochem/|Pascal Ochem]]**
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 ==== Past talks 2024 ==== ==== Past talks 2024 ====
 +
 +
 +**April 30 2024: [[https://www.math.uni-bielefeld.de/baake/|Michael Baake]]** //Hats, CAPs and Spectres//
 +
 +{{ seminar2024:20240430baake.pdf |slides}}
 +
 +{{ seminar2024:20240430baake.mp4 |video of the talk}}
 +
 +The recently discovered Hat is an aperiodic
 +monotile for the Euclidean plane, which needs a reflected
 +version for this property. The Spectre does not have this
 +(tiny) deficiency. We discuss the topological and dynamical
 +properties of the Hat tiling, how the CAP relates to it, and
 +what the long-range order of both tilings is. Finally, we
 +briefly describe the analogous structure for the Spectre tiling.
 +
 +
  
 **April 16 2024: [[https://dblp.org/pid/215/5120.html|Radosław Piórkowski]]** //Universal quantification in automatic structures—an ExpSpace-hard nut to crack// **April 16 2024: [[https://dblp.org/pid/215/5120.html|Radosław Piórkowski]]** //Universal quantification in automatic structures—an ExpSpace-hard nut to crack//