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start [2026/04/23 08:07] – anna.fridstart [2026/05/13 19:31] (current) – anna.frid
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 ==== Upcoming talks ====  ==== Upcoming talks ==== 
  
-**April 28 2026:  [[https://sites.google.com/ug.uchile.cl/espinoza|Bastiàn Espinoza]]** //The Thue-Morse word in base 3/2// +**POSTPONED <del>May 26 2026: Reem Yassawi</del>**
- +
-A rich family of symbolic dynamical systems of low complexity is given by automatic sequences. These sequences are obtained by feeding the base-$k$ expansions of integers, for a fixed integer base $k$, into a finite automaton. +
-In this talk, we turn to automatic sequences in rational bases, using as a guiding example a rational-base analogue of one of the most classical integer-base automatic words. +
-Namely, we consider the Thue--Morse word in base $3/2$, whose $n$-th term is given by the sum modulo 2 of the digits in the base-$3/2$ representation of $n$. +
-Our results show that, although this base-$3/2$ variant is substantially more complex than classical automatic words (for instance, it is not generated by iterating a single substitution, and its factor complexity grows superlinearly) it nevertheless retains several characteristic properties of the integer-automatic world. +
-More precisely, we prove uniform recurrence, establish the existence of letter frequencies, and show several combinatorial symmetries of its language analogous to those of the classical base-2 word. +
-Our approach relies on describing the word via the periodic iteration of two substitutions, studying the induced action of these substitutions on the $2$-adic integers, and applying Pontryagin duality on this group. +
- +
-This is joint work with Julien Cassaigne, Michel Rigo, and Manon Stipulanti. +
- +
-**May 12 2026: Léo Vivion** +
- +
-**May 26 2026: Reem Yassawi**+
  
 **June 9 2026:  [[https://kmlinux.fjfi.cvut.cz/~balkolub/| Ľubomíra Dvořáková]]** //Attractors of sequences coding beta-integers// **June 9 2026:  [[https://kmlinux.fjfi.cvut.cz/~balkolub/| Ľubomíra Dvořáková]]** //Attractors of sequences coding beta-integers//
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 Simple Parry sequences have been recently studied from this point of view and (not necessarily minimal) attractors of their prefixes have been described and a conjecture that attractors of alphabet size should be sufficient was stated. We prove this conjecture. Moreover, we provide attractors of prefixes of some particular form of binary non-simple Parry sequences. Simple Parry sequences have been recently studied from this point of view and (not necessarily minimal) attractors of their prefixes have been described and a conjecture that attractors of alphabet size should be sufficient was stated. We prove this conjecture. Moreover, we provide attractors of prefixes of some particular form of binary non-simple Parry sequences.
  
-**June 23 2026: Benoit Clôitre**+**June 23 2026: Benoit Cloitre**
  
 **July 7 2026: Delaram Moradi** **July 7 2026: Delaram Moradi**
  
 ==== Past talks 2026 ==== ==== Past talks 2026 ====
 +
 +
 +**May 12 2026: [[https://www-lmpa.univ-littoral.fr/~lvivion/|Léo Vivion]]** //New examples of words for which binomial complexities and subword complexity coincide//
 +
 +{{ seminar2026:20260512vivion.pdf |slides}}
 +
 +(The talk was not recorded at the speaker's request.)
 +
 +In 2015, Rigo and Salimov introduced a family of complexities that forms a scale between abelian complexity and factor complexity: the $k$-binomial complexities. In particular, they showed that Sturmian words satisfy the following remarkable combinatorial property: their $2$-binomial complexity is equal to their factor complexity. Since then, the only other known example satisfying this property is the Tribonacci word.
 +
 +In this talk, I will present some stability results for words whose $k$-binomial complexities coincide with their factor complexity, notably under letter deletion and a coloring operation. These stability properties allow to show that several well-known families of words also have their $2$-binomial complexity equal to their factor complexity.
 +
 +
 +**April 28 2026:  [[https://sites.google.com/ug.uchile.cl/espinoza|Bastiàn Espinoza]]** //The Thue-Morse word in base 3/2//
 +
 +{{ seminar2026:20260428espinoza.pdf |slides}}
 +
 +{{ seminar2026:20260428espinoza.mp4 |video of the talk}}
 +
 +
 +A rich family of symbolic dynamical systems of low complexity is given by automatic sequences. These sequences are obtained by feeding the base-$k$ expansions of integers, for a fixed integer base $k$, into a finite automaton.
 +In this talk, we turn to automatic sequences in rational bases, using as a guiding example a rational-base analogue of one of the most classical integer-base automatic words.
 +Namely, we consider the Thue--Morse word in base $3/2$, whose $n$-th term is given by the sum modulo 2 of the digits in the base-$3/2$ representation of $n$.
 +Our results show that, although this base-$3/2$ variant is substantially more complex than classical automatic words (for instance, it is not generated by iterating a single substitution, and its factor complexity grows superlinearly) it nevertheless retains several characteristic properties of the integer-automatic world.
 +More precisely, we prove uniform recurrence, establish the existence of letter frequencies, and show several combinatorial symmetries of its language analogous to those of the classical base-2 word.
 +Our approach relies on describing the word via the periodic iteration of two substitutions, studying the induced action of these substitutions on the $2$-adic integers, and applying Pontryagin duality on this group.
 +
 +This is joint work with Julien Cassaigne, Michel Rigo, and Manon Stipulanti.
 +
 +
  
 **April 14 2026: Idrissa Kaboré** //On modulo-recurrence and window complexity in infinite words// **April 14 2026: Idrissa Kaboré** //On modulo-recurrence and window complexity in infinite words//