Bridges between Automatic Sequences, Algebra and Number Theory

ag.algebraic-geometry co.combinatorics nt.number-theory
Start Date
End Date
Centre de Recherches Mathématiques 
Montréal, QC 
Meeting Type
school + workshop 
Contact Name


The aim of the school and workshop is to bring together graduate students, postdocs, and senior researchers working in the theory of automatic sequences or in areas that have some strong connection to automatic sequences to discuss their research and foster collaboration. The workshop will have a strong focus on the applications of automata and automatic sequences to algebra and to number theory.

As part of the Aisenstadt chair of the thematic semester, Boris Adamczewski will give a series of lectures on automatic sequences which will take place during these two weeks.


The school will consist of mini-courses on topics issued from combinatorics of words, algebra and number theory. This mini-courses will cover some of the algebraic and number theoretic background that will be useful for participants of the Workshop Bridges between Automatic Sequences and Algebra and Number Theory taking place the week after.

The mini-courses of the School will be given by:

– Yann Bugeaud (Université de Strasbourg) – Christophe Reutenauer (Université du Québec à Montréal) – Reem Yassawi (Université Paris Diderot-Paris 7)

Yann Bugeaud will give a minicourse about links between factor complexity, automatic numbers, transcendance and Diophantine approximation. Christophe Reutenauer will describe the correspondence between the theory Markoff numbers and the theory of Christoffel words. Reem Yassawi will give an introduction to automatic sequences, including in particular their links with algebra and number theory.

Other talks will be given by:

– Robbert Fokkink (Delft University of Technology) – Julien Leroy (Université de Liège) – Narad Rampersad (University of Winnipeg) – Eric Rowland (Hofstra University) – Štěpán Starosta (Czech Technical University in Prague) – Élise Vandomme (Université du Québec à Montréal)

We also plan sessions of exercises or experiments on computer allowing to develop intuitions on the presented mini-courses and talks.


The theory of finite automata naturally interacts, via automatic sequences and automatic sets, with algebra and number theory. Several advances have recently reinforced these deep links. The aim of this workshop is to allow researchers from different areas to meet and exchange about these advances. Among the themes to be covered by the invited talks are: transcendence and Diophantine analysis, arithmetic in positive characteristic, Galois theory of difference and differential equations, logic and model theory, analytic number theory, combinatorics and formal power series, group theory.


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