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start [2024/04/30 14:50] – 139.124.146.3start [2024/05/14 19:51] – 139.124.146.3
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-**April 30 2024: [[https://www.math.uni-bielefeld.de/baake/|Michael Baake]]** //Hats, CAPs and Spectres// 
  
-The recently discovered Hat is an aperiodic +**May 28 2024: [[https://www.lirmm.fr/~ochem/|Pascal Ochem]]**
-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.+
  
 +**June 11 2024: [[https://mwhiteland.github.io/|Markus Whiteland]]**
  
 +**June 25 2024: [[http://iml.univ-mrs.fr/~cassaign/|Julien Cassaigne]]**
 +
 +**July 9 2024: [[https://scholar.google.com.au/citations?user=C_02gXUAAAAJ&hl=en|Jamie Simpson]]**
 +
 +
 +==== Past talks 2024 ====
 **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// **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//
 +
 +{{ seminar2024:20240514rukavicka.pdf |slides}}
 +
 +{{ seminar2024:20240514rukavicka.mp4 |video of the talk}}
 +
  
 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 $k \geq 3$. 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 $k \geq 3$.
Line 40: Line 45:
 https://arxiv.org/abs/2312.10061 https://arxiv.org/abs/2312.10061
  
-**May 28 2024: [[https://www.lirmm.fr/~ochem/|Pascal Ochem]]** 
  
-**June 11 2024: [[https://mwhiteland.github.io/|Markus Whiteland]]**+**April 30 2024: [[https://www.math.uni-bielefeld.de/baake/|Michael Baake]]** //Hats, CAPs and Spectres//
  
-**June 25 2024: [[http://iml.univ-mrs.fr/~cassaign/|Julien Cassaigne]]**+{{ seminar2024:20240430baake.pdf |slides}}
  
-**July 9 2024: [[https://scholar.google.com.au/citations?user=C_02gXUAAAAJ&hl=en|Jamie Simpson]]**+{{ 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.
  
  
-==== Past talks 2024 ==== 
  
 **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//