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 ==== Upcoming talks ====  ==== Upcoming talks ==== 
  
 +**October 14 2025: Nicolas Bédaride**
  
 +**October 28 2025: Idrissa Kaboré**
  
-**May 20 2025: Pranjal Jain**+**November 11 2025: Aleksi Vanhatalo**
  
-**June 3 2025: Curtis Bright**+**November 25 2025: Ignacio Mollo** 
 + 
 +** December 9 2025: Florin Manea** 
 + 
 +**December 23 2025: Savinien Kreczman** 
 + 
 +**January 6 2025: Louis Marin** 
 + 
 + 
 +==== Past talks 2025 ==== 
 + 
 +**September 16 2025: Kaisei Kishi** //Net Occurrences in Fibonacci and Thue-Morse Words// 
 + 
 +{{ seminar2025:20250916kishi.pdf |slides}} 
 + 
 +{{ seminar2025:20250916kishi.mp4 |video of the talk}} 
 + 
 +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. 
 + 
 + 
 +**September 2 2025: Gandhar Joshi** //Monochromatic Arithmetic Progressions in Sturmian sequences// 
 + 
 +{{ seminar2025:20250902joshi.pdf |slides}} 
 + 
 +{{ seminar2025:20250902joshi.mp4 |video of the talk}} 
 + 
 +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.
  
-**June 17 2025: [[https://sites.google.com/view/noysofferaranov/bio|Noy Soffer Aranov]]** 
  
 **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//
  
-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.+{{ seminar2025:20250715krawczyk.pdf |slides}}
  
 +{{ seminar2025:20250715krawczyk.mp4 |video of the talk}}
  
  
-==== Past talks 2025 ====+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. 
 + 
 + 
 + 
 +**June 17 2025: [[https://sites.google.com/view/noysofferaranov/bio|Noy Soffer Aranov]]** //Escape of Mass of Sequences// 
 + 
 +{{ seminar2025:20250617aranov.pdf |slides}} 
 + 
 +{{ seminar2025:20250617aranov.mp4 |video of the talk}} 
 + 
 + 
 +One way to study the distribution of nested quadratic number fields satisfying fixed arithmetic relationships is through the evolution of continued fraction expansions. In the function field setting, it was shown by de Mathan and Teullie that given a quadratic irrational $\Theta$, the degrees of the periodic part of the continued fraction of $t^n\Theta$ are unbounded. Paulin and Shapira improved this by proving that quadratic irrationals exhibit partial escape of mass. Moreover, they conjectured that they must exhibit full escape of mass. We construct counterexamples to their conjecture in every characteristic. In this talk we shall discuss the technique of proof as well as the connection between escape of mass in continued fractions, Hecke trees, and number walls. This is part of joint works with Erez Nesharim and Uri Shapira and with Steven Robertson. 
 + 
 + 
 +**June 3 2025: [[https://www.curtisbright.com/|Curtis Bright]]** //Mathematical Problems with SATisfying Solutions// 
 + 
 +Automated reasoning tools have been effectively used to solve a variety of problems in discrete mathematics.  In this talk, I will introduce satisfiability (SAT) solvers and highlight a variety of problems in discrete mathematics that have been tackled with a SAT solver.  As a case study, I will demonstrate how a SAT solver can be used to make progress on a question arising in combinatorics on words involving North-East lattice paths. 
 + 
 +{{ seminar2025:20250603bright.pdf |slides}} 
 + 
 +{{ seminar2025:20250603bright.mp4 |video of the talk}} 
 + 
 + 
 +**May 20 2025: [[https://www.researchgate.net/profile/Pranjal-Jain-10|Pranjal Jain]]** //Partial Sums of Binary Subword-Counting Sequences// 
 + 
 +{{ seminar2025:20250520jain.pdf |slides}} 
 + 
 +{{ seminar2025:20250520jain.mp4 |video of the talk}} 
 + 
 + 
 +Let $w$ be a finite word over the alphabet $\{0,1\}$. For any natural number $n$, let $s_w(n)$ denote the number of occurrences of $w$ in the binary expansion of $n$ as a scattered subsequence. The talk aims to provide a systematic way of studying the growth of the partial sum $\sum_{n=0}^N (-1)^{s_w(n)}$ as $N \to \infty$. In particular, these techniques yield several classes of words $w$ with $\sum_{n=0}^N (-1)^{s_w(n)} = O(N^{1-\epsilon})$ for some $\epsilon >0$. We begin by motivating the ideas using the case of $w=01,011$. The talk is based on joint work with Shuo Li. 
 **May 6 2025: Jarkko Peltomäki** //The repetition threshold for ternary rich words// **May 6 2025: Jarkko Peltomäki** //The repetition threshold for ternary rich words//
  
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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 ====