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--- start [2026/03/31 15:03] – anna.frid
+++ start [2026/06/24 12:59] (current) – anna.frid
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 ==== Upcoming talks ====
+To be scheduled later
+<del>**July 7 2026: Delaram Moradi**</del>
-**April 14 2026: Idrissa Kaboré** //On modulo-recurrence and window complexity in infinite words//
+==== Past talks 2026 ====
+**June 23 2026: [[https://arxiv.org/search/math?searchtype=author&query=Cloitre,+B|Benoit Cloitre]]** //The Thue-Morse Transform//
-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.
+{{ seminar2026:20260623cloitre.pdf |slides}}
-**April 28 2026: [[https://kmlinux.fjfi.cvut.cz/~balkolub/| Ľubomíra Dvořáková]]** //Attractors of sequences coding beta-integers//
+{{ seminar2026:20260623cloitre.mp4 |video of the talk}}
-**May 12 2026: Léo Vivion**
-**May 26 2026: Reem Yassawi**
-**June 9 2026: Bastiàn Espinoza**
+We define a transform $T$ on binary words. Given a binary word, we use the positions of its zeros and ones to build a new binary word. Applied to the alternating word $a_0 = 0101\ldots$, the transform gives the Thue-Morse word. We then study the orbit $a_m = T^m(a_0)$, together with the sequences $u_m$ and $v_m$ giving the positions of the ones and the zeros in $a_m$. We obtain an explicit formula for $a_m(n)$ in terms of the binary digits of $n$ and $m-1$. From this formula we derive Prouhet-Tarry-Escott identities, composition formulas that generalize the identities for evil and odious numbers, and a recurrence formula for the factor complexity of $a_m$. We end with a few directions, such as applying the transform to the Fibonacci word, which yields the Fibonacci-Thue-Morse word.
-**July 7 2026: Delaram Moradi**
-==== Past talks 2026 ====
+**June 9 2026:  [[https://kmlinux.fjfi.cvut.cz/~balkolub/| Ľubomíra Dvořáková]]** //Attractors of sequences coding beta-integers//
+{{ seminar2026:20260609dvorakova.pdf |slides}}
+{{ seminar2026:20260609dvorakova.mp4 |video of the talk}}
+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.
+**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//
+{{ 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.
 **March 31 2026: [[https://sites.google.com/view/paulinacb|Paulina Cecchi Bernales]]** //Interplay between combinatorics and dynamical properties in minimal symbolic systems.