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 ==== Upcoming talks ====  ==== Upcoming talks ==== 
  
 +**September 2 2025: Gandhar Joshi**
  
-**June 17 2025: [[https://sites.google.com/view/noysofferaranov/bio|Noy Soffer Aranov]]** //Escape of Mass of Sequences//+**September 16 2025: Kaisei Kishi**
  
-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.+**October 28 2025: Idrissa Kaboré**
  
 +**November 11 2025: Aleksi Vanhatalo**
  
 +**November 25 2025: Ignacio Mollo**
 +
 +** December 9 2025: Florin Manea**
 +
 +**December 23 2025: Savinien Kreczman**
 +
 +
 +==== Past talks 2025 ====
  
 **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// **June 3 2025: [[https://www.curtisbright.com/|Curtis Bright]]** //Mathematical Problems with SATisfying Solutions//