Sebastián Barbieri Lemp

## Overview

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.

## Publications

Preprints

• [2020] Gibbsian representations of continuous specifications: the theorems of Kozlov and Sullivan revisited.
with Ricardo Gómez, Brian Marcus, Tom Meyerovitch and Siamak Taati.
• [2019] Markovian properties of continuous group actions: algebraic actions, entropy and the homoclinic group.
with Felipe García Ramos and Hanfeng Li.

Journals

• [to appear] On the entropies of subshifts of finite type on countable amenable groups.
To appear in Groups, Geometry and Dynamics.
• [to appear] A hierarchy of topological systems with completely positive entropy.
with Felipe García-Ramos. To appear in Journal d'Analyse Mathématique.
• [2020] Equivalence of relative Gibbs and relative equilibrium measures for actions of countable amenable groups.
with Ricardo Gómez, Brian Marcus and Siamak Taati. in Nonlinearity.
• [2019] A geometric simulation theorem on direct products of finitely generated groups.
In Discrete Analysis.
• [2019] A generalization of the simulation theorem for semidirect products.
with Mathieu Sablik. In Ergodic Theory and Dynamical Systems.
• [2019] Realization of aperiodic subshifts and uniform densities in groups.
with Nathalie Aubrun and Stéphan Thomassé. In Groups, Geometry and Dynamics.
• [2017] A notion of effectiveness for subshifts on finitely generated groups.
with Nathalie Aubrun and Mathieu Sablik. In Theoretical Computer Science.

International Conferences

• [2019] The domino problem is undecidable on surface groups.
with Nathalie Aubrun and Etienne Moutot. In MFCS
• [2016] The domino problem for self-similar structures.
with Mathieu Sablik. In CIE.
• [2016] The group of reversible Turing machines.
with Jarkko Kari and Ville Salo. In AUTOMATA.

Book chapters

• [2018] About the Domino Problem for Subshifts on Groups.
with Nathalie Aubrun and Emmanuel Jeandel. In Sequences, Groups, and Number Theory.

Thesis and Memoires

• [2017] Shift spaces on groups: computability and dynamics, Thesis.
• [2014] Tilings on different structures: exploration towards two problems, Mémoire M2.
• [2014] Subshifts generados por sustituciones multidimensionales, Memoria ingeniería Universidad de Chile.

## Work in progress ( last updated Nov 2019 )

• A long version of the Automata paper "The group of reversible Turing machines". With Jarkko Kari and Ville Salo.
• A generalization of the simulation theorem of Aubrun and Sablik to products of arbitrary finitely generated groups. This is work in progress with Mathieu Sablik.
• Extending the results about the domino problem for surface groups to word-hyperbolic groups and other classes. This is work in progress with Nathalie Aubrun and Laurent Bartholdi.
• Studying the symbolic dynamical systems that can arise from polygonal partitions of the torus and the $\mathbb{Z}^2$-translation action. This is joint work with Sébastien Labbé.
• Classifying the class of asymptotic pairs in symbolic systems which are statistically indistinguishable from the point of view of word combinatorics. This is work in progress with Sébastien Labbé and Štěpán Starosta.