Sebastián Barbieri Lemp

Welcome to my research page, here you can find my personal information, publications and some miscellaneous links.

I just finished my PhD thesis in ENS Lyon, In August I'm starting a postdoc in the University of British Columbia. I'll soon be migrating to a new webpage. My research interests are: dynamical systems, symbolic dynamics, tilings, substitutions, computability, group theory and cellular automata.

My CV can be found clicking here
Email:
Bureau 274 LUG
46 allée d’Italie
69007 Lyon
See [directions]

## Research

Journals

• A notion of effectiveness for subshifts on finitely generated groups.[pdf][doi] in Theoretical Computer Science 2017, With Nathalie Aubrun and Mathieu Sablik.
• (To appear in Ergodic Theory and Dynamical Systems) A generalization of the simulation theorem for semidirect products[pdf], With Mathieu Sablik.
• (To appear in Groups, Geometry and Dynamics) Realization of aperiodic subshifts and densities in groups.[pdf], With Nathalie Aubrun and Stéphan Thomassé.
International Conferences:

• The domino problem for self-similar structures.[pdf][doi] in Computing in Europe 2016, With Mathieu Sablik.
• The group of reversible Turing machines.[pdf][doi] in AUTOMATA 2016, With Jarkko Kari and Ville Salo.
Ongoing and submitted

• A geometric simulation theorem on direct product of finitely generated groups [pdf]
Work in progress:

• A long version of the Automata paper The group of reversible Turing machines. With Jarkko Kari and Ville Salo. We've added some extra theorems and detailed proofs of the results announced in the automata version.
• A study of automorphism groups of algebraic subshifts. So far I have some decomposition theorems, a class of algebraic subshifts for which the automorphism groups are easy to characterize in terms of the Unit group of a quotient ring and a few computability results. I am exploring a wide definition of deterministic sets as a replacement for the Fourier decomposition given by Pontryagin duality if the alphabet were $\mathbb{C}$.
• A project to study computable topologies on the set of subshifts on $\mathbb{Z}^2$. For many aspects, the usual Hausdorff topology given by the convergence of the language in every finite window is insufficient to study interesting sets such as sofic or effective subshifts. My goal is to define different topologies linked to computability restrictions (such as restrictions on the projective subdynamics) in order to get more insight on open problems such as whether all sofic subshifts admit same entropy SFT extensions.
Thesis and Memoires:

• Shift spaces on groups: computability and dynamics[pdf], PhD Thesis at ENS de Lyon, June 2017.
• Tilings on different structures: exploration towards two problems.[pdf], Mémoire de M2 de l'ENS de Lyon, June 2014.
• Subshifts generados por sustituciones multidimensionales.[pdf], Memoria ingeniería Universidad de Chile, July 2014.

## Talks

• A strongly aperiodic SFT in the Grigorchuk group.[pdf], Pingree Park, July 2017.
• Shift spaces on groups: computability and dynamics.[pdf], PhD thesis defense, June 2017.
• Realizability of non-expansive dynamics and applications.[pdf], Workshop dyadisc Amiens, June 2017.
• Symbolic dynamics and simulation theorems.[pdf], Séminaire Automata IRIF, May 2017.
• Strongly aperiodic subshifts in countable groups.[pdf], Séminaire Ernest Marseille, April 2017.
• Strongly aperiodic subshifts in countable groups.[pdf], Séminaire de combinatoire et théorie des nombres DOUA, March 2017.
• The torsion problem for the automorphism group of a full $\mathbb{Z}^d$-shift and its topological fullgroup. [pdf], Wroclaw, March 2017.
• The group of reversible Turing machines and the torsion problem for $\operatorname{Aut}(\mathcal{A}^{\mathbb{Z}^d})$ and related topological fullgroups. [pdf], CMM, December 2016.
• The domino problem for self-similar structures. [pdf], CIE, June 2016.
• The group of reversible Turing machines.[pdf], AUTOMATA, June 2016.
• Une courte preuve de l'existence des subshifts fortement apériodiques sur les groupes dénombrables. [in french] [pdf], Interactions, ENS de Lyon, May 2016.
• Que pensent les mosaïques de la monotonie ? [in french][pdf], Séminaire détente matématique ENS de Lyon, March 2016.
• A short proof of the existence of non-empty strongly aperiodic subshifts over $\{0,1\}$ in countable groups.[pdf], Chambery, January 2016.
• A short proof of the existence of non-empty strongly aperiodic subshifts over $\{0,1\}$ in countable groups.[pdf], Amiens, December 2015.
• The domino problem for structures between $\mathbb{Z}$ and $\mathbb{Z}^2$.[pdf], Paris-est Creteil, November 2015.
• The domino problem for structures between $\mathbb{Z}$ and $\mathbb{Z}^2$.[pdf], University of Turku, October 2015.
• Subshifts in groups: From square-free words on graphs to aperiodic subshifts.[pdf], Rouen, October 2015.
• Effectiveness and aperiodicity of subshifts.[pdf], Fontainebleau, Journées Calculabilitées, April 2015.
• Effectiveness in finitely generated groups.[pdf], Paris, LIAFA, November 2014.
Posters:

• The domino problem for fractal subsets between $\mathbb{Z}$ and $\mathbb{Z}^2$.[pdf], Paris, Journées GDR-IM, january 2016.
• Effectiveness in finitely generated groups.[pdf], Chile, Workshop on Symbolic Dynamics on finitely presented Groups, december 2014.