PIMS office 4218
2207 Main Mall
Vancouver, BC
V6T 174.

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.

A generalization of the simulation theorem for semidirect products.[pdf][doi] in Ergodic Theory and Dynamical Systems 2018, 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.

Submitted:

A geometric simulation theorem on direct product of finitely generated groups[pdf]

A hiearchy of topological systems with completely positive entropy[pdf], with Felipe García-Ramos.

Book chapters:

About the Domino Problem for Subshifts on Groups. Chapter 9 in Sequences, Groups, and Number Theory. [doi] With Nathalie Aubrun and Emmanuel Jeandel.

Work in progress:

A long version of the Automata paper "The group of reversible Turing machines". With Jarkko Kari and Ville Salo.

A study of automorphism groups of algebraic subshifts. This is work in progress with many people.

Reinterpreting Highman's embedding theorem in dynamical terms.

The domino problem for surface groups, and more generally, for hyperbolic groups. This is work in progress with Nathalie Aubrun and Etienne Moutot.

A project to translate DLR equations to larger classes of group actions.

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

Mini courses:

Dinámica simbólica sobre los grupos. [in spanish] [pdf1][pdf2][pdf3][pdf4], Ciudad de México, Escuela de invierno en grupos y dinámica en México, january 2018.

Talks:

A strongly aperiodic SFT in the Grigorchuk group.[pdf], Toulouse, March 2018.

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.

Links

The webpage for the course MATH253:103 I'm teaching at UBC.

Project Euler, a page with hundreds of math problems. My friend key:766412_FJHCB0aQSNlb36NDq86FcmayO5Lc7TzT