Talks

2024

1. Are all dynamical properties of $\mathbb{Z}^2$-SFTs undecidable?

   Nicanor Carrasco-Vargas

   Feb 2024

   Poster for thematic month at CIRM, France: Discrete Mathematics & Computer Science: Groups, Dynamics, Complexity, Words.

   Poster Website
2. A recursion-theoretic invariant for subshifts

   Nicanor Carrasco-Vargas

   Feb 2024

   Talk for thematic month at CIRM, France: Discrete Mathematics & Computer Science: Groups, Dynamics, Complexity, Words.

   Slides Website

2023

1. Medvedev degrees of effective subshifts on groups

   Nicanor Carrasco-Vargas

   Mar 2023

   Journées annuelles SDA2, Toulouse, France

   Abs Slides Website

   It is known that the class of effective subshifts in $\mathbb{Z}$ can attain all $\Pi_1$ Medvedev degrees. In this talk we will discuss how this result extends to the class of finitely generated groups with decidable word problem. This involves codifying translation-like actions by $\mathbb{Z}$ as a subshift, and takes us to the problem of the computability of translation-like actions on locally finite graphs

2. Medvedev degrees and subshifts

   Nicanor Carrasco-Vargas

   Jul 2023

   16th International Conference on Computability, Complexity and Randomness. Kochel, Germany

   Abs PDF Slides Website

   The abstract is in the "pdf" button

3. Un invariante para subshifts de naturaleza recursiva

   Nicanor Carrasco-Vargas

   Sep 2023

   Seminario de Sistemas Dinámicos de Santiago, Santiago, Chile

   Abs Website

   En 1974 Hanf y Myers exhibiron un subshift de tipo finito en $\mathbb{Z}^2$ cuyas configuraciones son todas incalculables en el sentido de la teoria de la recursión. En esta charla discutiremos cómo este fenómeno se captura con un invariante dinámico para subshifts, el invariante m. Este invariante comparte algunas propiedades con la entropía topológica como no aumentar por factores. También se relaciona con otras propiedades de origen dinámico y topológico tales como la aperiodicidad o la existencia puntos aislados en el espacio de todos los subshifts.

4. Un invariante para subshifts de naturaleza recursiva

   Nicanor Carrasco-Vargas

   Dec 2023

   Encuentro sociedad matemática de chile 2023, Santiago, Chile

   Abs PDF Slides Website

   The abstract is in the "pdf" button.