Sebastián Barbieri Lemp


My research aims to study the rich interplay between the dynamics of group actions and computability to further understand both phenomena from a unified perspective.

A more detailed exposition can be found by clicking on my self portrait on the right.


Effective dynamical systems beyond dimension zero and factors of SFTs.
With Nicanor Carrasco-Vargas and Cristóbal Rojas.
Soficity of free extensions of effective subshifts.
With Mathieu Sablik and Ville Salo.
The group of reversible Turing machines: subgroups, generators and computability.
With Jarkko Kari and Ville Salo.
Chaos in Bidimensional Models with Short-Range.
With Rodrigo Bissacot, Gregório Dalle Vedove and Philippe Thieullen.
Groups with self-simulable zero-dimensional dynamics.
With Mathieu Sablik and Ville Salo.


Indistinguishable asymptotic pairs and multidimensional Sturmian configurations.
With Sébastien Labbé.
Ergodic Theory and Dynamical Systems, to appear
Aperiodic subshifts of finite type on groups which are not finitely generated.
Proceedings of the American Mathematical Society, 151:3839-3843, 2023
The Lanford–Ruelle theorem for actions of sofic groups.
With Tom Meyerovitch.
Transactions of the American Mathematical Society, 376(2):1299-9947, 2023.
Markovian properties of continuous group actions: algebraic actions, entropy and the homoclinic group.
With Felipe García Ramos and Hanfeng Li.
Advances in Mathematics, 397(108196):1–52, 2022.
On the entropies of subshifts of finite type on countable amenable groups.
Groups, Geometry and Dynamics, 15(2):607–638, 2021.
A hierarchy of topological systems with completely positive entropy.
With Felipe García-Ramos.
Journal d'Analyse Mathématique, 143(2):639-680, 2021.
A characterization of Sturmian sequences by indistinguishable asymptotic pairs
With Sébastien Labbé and Štěpán Starosta.
European Journal of Combinatorics, 95(103318):1-22, 2021.
Gibbsian representations of continuous specifications: the theorems of Kozlov and Sullivan revisited.
With Ricardo Gómez, Brian Marcus, Tom Meyerovitch and Siamak Taati.
Communications in Mathematical Physics, 382(2):1111–1164, 2021.
Equivalence of relative Gibbs and relative equilibrium measures for actions of countable amenable groups.
With Ricardo Gómez, Brian Marcus and Siamak Taati.
Nonlinearity, 33(5):2409–2454, 2020.
A geometric simulation theorem on direct products of finitely generated groups.
Discrete Analysis, 9:25, 2019.
A generalization of the simulation theorem for semidirect products.
With Mathieu Sablik.
Ergodic Theory and Dynamical Systems, 39(12):3185–3206, 2019.
Realization of aperiodic subshifts and uniform densities in groups.
With Nathalie Aubrun and Stéphan Thomassé.
Groups, Geometry, and Dynamics, 13(1):107–129, 2019.
A notion of effectiveness for subshifts on finitely generated groups.
With Nathalie Aubrun and Mathieu Sablik.
In Theoretical Computer Science, 661:35–55, 2017.

Conference Proceedings

The domino problem is undecidable on surface groups.
With Nathalie Aubrun and Etienne Moutot.
44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019), pages 1–14, 2019.
The domino problem for self-similar structures.
With Mathieu Sablik.
Pursuit of the Universal (CIE 2016), pages 205–214, 2016.
The group of reversible Turing machines.
With Jarkko Kari and Ville Salo.
Cellular Automata and Discrete Complex Systems (AUTOMATA 2016), pages 49–62, 2016.

Book chapters

About the Domino Problem for Subshifts on Groups.
With Nathalie Aubrun and Emmanuel Jeandel.
Sequences, Groups, and Number Theory, pages 331–389. Springer International Publishing, 2018.

Thesis and Memoires

Shift spaces on groups: computability and dynamics.
Theses, Université de Lyon (ENS de Lyon), June 2017.
Tilings on different structures: exploration towards two problems.
Mémoire Master 2, 2014.
Subshifts generados por sustituciones multidimensionales.
Memoria ingeniería Universidad de Chile, 2014.