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Hi! I am Antonin Callard and I am a “maître de conférences” (≃ assistant professor) studying symbolic dynamics and its connections to computability and complexity theory. I am currently part of the ESCAPE team at the LIRMM laboratory (Université de Montpellier, France). If you want to learn more about me (or get my email address), you can visit this page. If you want to read my personal blog, you can go here. In any case, welcome!
Agenda
Recent activities
We wrote a preprint with Andrei Romashchenko, Véronique Terrier and Pascal Vanier on the use of communication complexity in tilings. In particular, we focus on the notion of unambiguous non-determinism, and prove that the class of picture languages UREC contains a language that does not even belong in coREC.
Quite recently, I also finally completed some work on sufficient conditions for the multidimensional soficity of shift spaces with Pierre Guillon, Léo Paviet Salomon and Pascal Vanier. It had been in-the-making for quite a while! These conditions are phrased in terms of $S$-adic shifts, in which the increasingly large alphabets of the intermediate substitutions allow to quantify the amount of “useful information” in the configurations of a shift. This is a much more flexible formalism for the second half of my thesis, and a preprint is available on the arXiv!