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start [2025/04/22 14:24] – 139.124.146.3start [2025/06/09 16:53] (current) – 139.124.146.3
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-**May 6 2025: Jarkko Peltomäki**+**June 17 2025: [[https://sites.google.com/view/noysofferaranov/bio|Noy Soffer Aranov]]** //Escape of Mass of Sequences//
  
-**May 20 2025: Pranjal Jain**+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: Curtis Bright** 
  
-**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//
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 ==== Past talks 2025 ==== ==== Past talks 2025 ====
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 +**June 3 2025: [[https://www.curtisbright.com/|Curtis Bright]]** //Mathematical Problems with SATisfying Solutions//
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 +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.
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 +{{ seminar2025:20250603bright.pdf |slides}}
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 +{{ seminar2025:20250603bright.mp4 |video of the talk}}
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 +**May 20 2025: [[https://www.researchgate.net/profile/Pranjal-Jain-10|Pranjal Jain]]** //Partial Sums of Binary Subword-Counting Sequences//
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 +{{ seminar2025:20250520jain.pdf |slides}}
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 +{{ seminar2025:20250520jain.mp4 |video of the talk}}
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 +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.
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 +**May 6 2025: Jarkko Peltomäki** //The repetition threshold for ternary rich words//
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 +{{ seminar2025:20250506peltomaki.pdf |slides}}
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 +{{ seminar2025:20250506peltomaki.mp4 |video of the talk}}
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 +In the recent years, it has been popular to determine the least critical exponent in specific families of infinite words. In this talk, I will explain what is known about the least critical exponents for infinite words that are rich in palindromes. In particular, I will outline the proof of our result that the least critical exponent for ternary rich infinite words equals $1 + 1/(3 - \mu) \approx 2.25876324$, where $\mu$ is the unique real root of the polynomial $x^3 - 2x^2 - 1$. This result is based on proving a structure theorem for ternary rich infinite words that avoid $16/7$-powers. In addition, I discuss some recent progress on determining the least asymptotic critical exponents for rich infinite words.
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 +Joint work with L. Mol and J. D. Currie.
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 +
  
 **April 22 2025: [[https://sites.google.com/view/beeri-greenfeld|Be'eri Greenfeld]]** //On the Complexity of Infinite Words// **April 22 2025: [[https://sites.google.com/view/beeri-greenfeld|Be'eri Greenfeld]]** //On the Complexity of Infinite Words//