Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revisionPrevious revision
Next revision		Previous revision
start [2026/03/31 15:01] – anna.fridstart [2026/05/13 19:31] (current) – anna.frid
Line 22: Line 22:
 ==== Upcoming talks ====  ==== Upcoming talks ==== 
  
 +**POSTPONED <del>May 26 2026: Reem Yassawi</del>**
  
 +**June 9 2026:  [[https://kmlinux.fjfi.cvut.cz/~balkolub/| Ľubomíra Dvořáková]]** //Attractors of sequences coding beta-integers//
  
-**April 14 2026: Idrissa Kaboré** //On modulo-recurrence and window complexity in infinite words//+String attractor is an intensively studied object in Combinatorics on Words. 
 +In our talk, we will recall known results and also some previously used techniques. 
 +We will then describe minimal string attractors of prefixes of simple Parry sequences. 
 +These sequences form a coding of distances between consecutive beta-integers in numeration systems with a real base beta. 
 +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.
  
-In this talk, first, I will recall the notions of modulo-recurrent words and of window complexity. These notions are introduced in 2007. Then, I present some properties of these notions. After that, I will present the notions of uniform modulo-recurrence and of strong modulo-recurrence. These notions are defined recently in a joint work with Julien Cassaigne. Sturmian words are uniformly (resp. strongly) modulo-recurrent words. Then, I will address the window complexity of the Thue-Morse. To finish, I will present a recurrent aperiodic word with bounded window complexity.+**June 23 2026: Benoit Cloitre**
  
-**April 28 2026: [[https://kmlinux.fjfi.cvut.cz/~balkolub/| Ľubomíra Dvořáková]]** //Attractors of sequences coding beta-integers//+**July 7 2026: Delaram Moradi**
  
-**May 12 2026: Léo Vivion**+==== Past talks 2026 ====
  
-**May 26 2026: Reem Yassawi** 
  
-**June 9 2026: Bastiàn Espinoza**+**May 12 2026: [[https://www-lmpa.univ-littoral.fr/~lvivion/|Léo Vivion]]** //New examples of words for which binomial complexities and subword complexity coincide//
  
-**July 7 2026: Delaram Moradi**+{{ 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// 
 + 
 + 
 +{{ seminar2026:20260414kabore.pdf |slides}} 
 + 
 +{{ seminar2026:20260414kabore.mp4 |video of the talk}} 
 + 
 +In this talk, first, I will recall the notions of modulo-recurrent words and of window complexity. These notions are introduced in 2007. Then, I present some properties of these notions. After that, I will present the notions of uniform modulo-recurrence and of strong modulo-recurrence. These notions are defined recently in a joint work with Julien Cassaigne. Sturmian words are uniformly (resp. strongly) modulo-recurrent words. Then, I will address the window complexity of the Thue-Morse. To finish, I will present a recurrent aperiodic word with bounded window complexity.
  
-==== Past talks 2026 ==== 
  
 **March 31 2026: [[https://sites.google.com/view/paulinacb|Paulina Cecchi Bernales]]** //Interplay between combinatorics and dynamical properties in minimal symbolic systems. **March 31 2026: [[https://sites.google.com/view/paulinacb|Paulina Cecchi Bernales]]** //Interplay between combinatorics and dynamical properties in minimal symbolic systems.
Line 45: Line 83:
 {{ seminar2026:20260331cecchi-bernales.pdf |slides}} {{ seminar2026:20260331cecchi-bernales.pdf |slides}}
  
-{{ seminar2026:20260331cecchi-bernales |video of the talk}}+{{ seminar2026:20260331cecchi-bernales.mp4 |video of the talk}}
  
 Symbolic systems, also known as subshifts, are topological dynamical systems whose phase space consists of infinite sequences of symbols, evolving under the action of the (left) shift transformation. As infinite words, the elements of a symbolic system possess combinatorial properties associated with their language, and it is natural to ask how these combinatorial properties determine or interact with the properties of the system as a dynamical system, or vice versa. In this talk, I will briefly review the basic notions of symbolic systems and some classical results which connect their combinatorial and dynamical properties, particularly for subshifts generated by substitutions. I will then present more recent results illustrating the impact of combinatorics on the spectral properties of minimal subshifts. In these results, combinatorial objects such as extension graphs or coboundaries will play an important role. This is a part of a joint work with V. Berthé and B. Espinoza. Symbolic systems, also known as subshifts, are topological dynamical systems whose phase space consists of infinite sequences of symbols, evolving under the action of the (left) shift transformation. As infinite words, the elements of a symbolic system possess combinatorial properties associated with their language, and it is natural to ask how these combinatorial properties determine or interact with the properties of the system as a dynamical system, or vice versa. In this talk, I will briefly review the basic notions of symbolic systems and some classical results which connect their combinatorial and dynamical properties, particularly for subshifts generated by substitutions. I will then present more recent results illustrating the impact of combinatorics on the spectral properties of minimal subshifts. In these results, combinatorial objects such as extension graphs or coboundaries will play an important role. This is a part of a joint work with V. Berthé and B. Espinoza.