Research
I am interested in symbolic dynamics, combinatorics on words, automata theory and semigroup theory, in particular profinite semigroups. My work also has connections with group theory and ergodic theory. I am especially interested in the various connections between these areas. My research also has a strong experimental component, using software like SageMath, Python and Gap to guide my research.News
- Algebraic aspects of symbolic dynamics 2026. The aim of this workshop is to gather researchers interested in various algebraic aspects of symbolic dynamics to share their point of view and present their latest results. The event will take place in Porto from July 13 to 17, 2026. For more information, see the website of the conference: https://www.irif.fr/en/seminaires/algebraic-aspects-of-symbolic-dynamics-2026/index.
Abstract
The interplay of symbolic dynamics with algebra unfolds in a variety of ways, reflecting the overall richness of the fields. This includes the study of dynamical invariants like dimension groups, associated with the space of invariant measures, or Schützenberger groups, associated with the structure of free profinite semigroups; structural work on automorphism groups of symbolic systems, which also relate to semigroup theory via the construction of Ellis semigroups; relationships with subgroups of the free group, for instance via the theory of codes; cohomological methods linked with cocycles and coboundary, often applied to the study of continuous eigenvalues of symbolic systems; various results exploring the relationship between automatic sequences and power series over finite fields; algebraic methods used in the study of specific systems, like interval exchanges or hypercubic billiards; or the study of symbolic systems, particularly of finite type, over general classes of groups.