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start [2025/07/15 20:32] – 82.66.107.61start [2025/09/17 06:29] (current) – 82.66.107.61
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 ==== Upcoming talks ====  ==== Upcoming talks ==== 
  
-**September 2 2025: Gandhar Joshi** +**October 14 2025: Nicolas Bédaride**
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-**September 16 2025: Kaisei Kishi**+
  
 **October 28 2025: Idrissa Kaboré** **October 28 2025: Idrissa Kaboré**
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 **December 23 2025: Savinien Kreczman** **December 23 2025: Savinien Kreczman**
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 +**January 6 2025: Louis Marin**
  
  
 ==== Past talks 2025 ==== ==== Past talks 2025 ====
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 +**September 16 2025: Kaisei Kishi** //Net Occurrences in Fibonacci and Thue-Morse Words//
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 +{{ seminar2025:20250916kishi.pdf |slides}}
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 +{{ seminar2025:20250916kishi.mp4 |video of the talk}}
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 +In a string $T$, an occurrence of a substring $S=T[i ... j]$ is a net occurrence if $S$ is repeated in $T$, while both left extension $T[i-1, ... j]$ and right extension $T[i, ... j+1]$ are unique in $T$. The number of net occurrences of $S$ in $T$ is called its net frequency. Compared with ordinary frequency, net frequency highlights the more significant occurrences of $S$ in $T$. In this talk, I will present several properties of net occurrences and describe techniques to identify all the net occurrences in Fibonacci and Thue-Morse words. In particular, I will explain the technique to characterize the occurrences of smaller-order Fibonacci and Thue-Morse words. This is a joint work with Peaker Guo.
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 +**September 2 2025: Gandhar Joshi** //Monochromatic Arithmetic Progressions in Sturmian sequences//
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 +{{ seminar2025:20250902joshi.pdf |slides}}
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 +{{ seminar2025:20250902joshi.mp4 |video of the talk}}
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 +This is joint work with Dan Rust. We define Monochromatic arithmetic progression (MAP) as the repetition of a symbol (traditionally colour) with a constant difference in a sequence. We study thresholds of the lengths of MAPs in the Fibonacci word in our paper https://doi.org/10.1016/j.tcs.2025.115391, which not only resolves a few problems left open by previous works revolving around MAPs in symbolic sequences but also reveals a straightforward method to find a formula that finds longest lengths of MAPs for all Sturmians. This extension is dealt with in the author's PhD thesis.
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 **July 15 2025: [[https://apacz.matinf.uj.edu.pl/users/1719-elzbieta-krawczyk|Elżbieta Krawczyk]]**  //Quasi-fixed points of substitutions and substitutive systems// **July 15 2025: [[https://apacz.matinf.uj.edu.pl/users/1719-elzbieta-krawczyk|Elżbieta Krawczyk]]**  //Quasi-fixed points of substitutions and substitutive systems//
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-We study automatic sequences and automatic systems (symbolic dynamical systems) generated by general constant length (nonprimitive) substitutions. While an automatic system is typically uncountable, the set of automatic sequences is countable, implying that most sequences within an automatic system are not themselves automatic. We provide a complete classification of automatic sequences that lie in a given automatic system in terms of the so-called quasi-fixed points of the substitution defining the system. Quasi-fixed points have already appeared implicitly in a few places (e.g. in the  study of substitutivity of lexicographically minimal points in substitutive systems or in the study of subsystems of substitutive systems) and they have been described in detail by Shallit and Wang and, more recently, B\'eal, Perrin, and Restivo . We conjecture that a similar statement holds for general nonconstant length substitutions.+We study automatic sequences and automatic systems (symbolic dynamical systems) generated by general constant length (nonprimitive) substitutions. While an automatic system is typically uncountable, the set of automatic sequences is countable, implying that most sequences within an automatic system are not themselves automatic. We provide a complete classification of automatic sequences that lie in a given automatic system in terms of the so-called quasi-fixed points of the substitution defining the system. Quasi-fixed points have already appeared implicitly in a few places (e.g. in the  study of substitutivity of lexicographically minimal points in substitutive systems or in the study of subsystems of substitutive systems) and they have been described in detail by Shallit and Wang and, more recently, Béal, Perrin, and Restivo . We conjecture that a similar statement holds for general nonconstant length substitutions.
  
  
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 ==== Archives 2024 ==== ==== Archives 2024 ====
  
-The talks of 2023 are available [[2024|here]].+The talks of 2024 are available [[2024|here]].
  
 ==== Archives 2023 ==== ==== Archives 2023 ====