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 [2025/10/06 09:36] – 82.66.107.61start [2025/11/07 11:17] (current) – anna.frid
Line 22: Line 22:
 ==== Upcoming talks ====  ==== Upcoming talks ==== 
  
-**October 14 2025: Antoine Julien** //On balance properties of hypercubic billiard words//+**November 11 2025: [[https://www.utu.fi/en/people/aleksi-vanhatalo|Aleksi Vanhatalo]]** //Exponents of words under injective morphisms//
  
-This presentation is concerned with hypercubic billiards with irrational trajectories. In this talk, I will present the relationship between balance properties in hypercubic billiards, and subshift cohomology.+A very common problem type in combinatorics on words is to construct words (under constraints) that avoid repetition. This is often done by constructing suitable morphisms. 
 +Here we flip the setup: we ask how good morphisms are at introducing repetitions into words. Periodic morphisms are trivially very good at this, but how about less trivial classes of morphisms?
  
-More precisely, I will define cohomology for subshifts and (time permitting) illustrate with examples of how cohomology has previously been used in symbolic dynamics. Then, I will present the link between cohomology and balance for billiard sequences. Finally, I will explain how results of Kellendonk and Sadun on the dimension of some cohomology spaces implies that billiard words in cubes of dimension at least 3 cannot be balanced on all factors. +We consider a few variations of this question. We characterize finite words that do not have an upper bound on fractional or integer exponents when mapped via injective morphisms. Then we consider the asymptotic critical exponent of infinite words. While we consider all finite alphabet sizes, these variations are better understood in the binary case.  
-  +This talk is an extended version of the one presented at DLT 2025. It is based on joint work with Eva Foster and Aleksi Saarela, and on ongoing research.
-In the case of billiards in the cube, we also showed (using other methods) that these sequences are not balanced on factors of length 2. +
-  +
-Joint work with Nicolas Bédaride and Valérie Berthé.+
  
-**October 28 2025: Idrissa Kaboré** 
  
-**November 11 2025: Aleksi Vanhatalo** 
  
 **November 25 2025: Ignacio Mollo** **November 25 2025: Ignacio Mollo**
Line 49: Line 45:
  
 **February 17 2026: Steven Robertson** **February 17 2026: Steven Robertson**
 +
 +**March 03 2026: Ingrid Vukusic**
 +
 +**March 17 2026: Gwenael Richomme**
 +
 +**March 30 2026: Paulina Cecchi Bernales**
 +
 +**April 14 2026: Idrissa Kaboré** //On modulo-recurrence and window complexity in infinite words//
 +
 +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.
 +
 +**April 28 2026: [[https://kmlinux.fjfi.cvut.cz/~balkolub/| Ľubomíra Dvořáková]]** //Attractors of sequences coding beta-integers//
 +
 +
  
 ==== Past talks 2025 ==== ==== Past talks 2025 ====
 +
 +**October 14 2025: [[https://www.nord.no/en/about/employees/antoine-laurent-christophe-julien|Antoine Julien]]** //On balance properties of hypercubic billiard words//
 +
 +
 +{{ seminar2025:20251014julien.pdf |slides}}
 +
 +{{ seminar2025:20251014julien.mp4 |video of the talk}}
 +
 +This presentation is concerned with hypercubic billiards with irrational trajectories. In this talk, I will present the relationship between balance properties in hypercubic billiards, and subshift cohomology.
 +
 +More precisely, I will define cohomology for subshifts and (time permitting) illustrate with examples of how cohomology has previously been used in symbolic dynamics. Then, I will present the link between cohomology and balance for billiard sequences. Finally, I will explain how results of Kellendonk and Sadun on the dimension of some cohomology spaces implies that billiard words in cubes of dimension at least 3 cannot be balanced on all factors.
 + 
 +In the case of billiards in the cube, we also showed (using other methods) that these sequences are not balanced on factors of length 2.
 + 
 +Joint work with Nicolas Bédaride and Valérie Berthé.
 +
 +
  
 **September 16 2025: Kaisei Kishi** //Net Occurrences in Fibonacci and Thue-Morse Words// **September 16 2025: Kaisei Kishi** //Net Occurrences in Fibonacci and Thue-Morse Words//