I graduated in electronics engineering from the University of the Basque Country (EHU/UPV), as well as in physics from the National University of Distance Education of Spain (UNED). After a short teaching experience at secondary school, I completed a master in quantum science and technologies at EHU/UPV, my dissertation being focussed on analog quantum simulations in trapped ions (https://arxiv.org/abs/1802.01853). In 2019, I joined the School of Mathematics and Statistics at the Open University, where I am pursuing a PhD under the supervision of Prof. Uwe Grimm and Dr. Ian Short. I am a member of the Aperiodic Order Research Group as well as the Dynamical Systems Seminar.
My mathematical research interests lie, mainly, in dynamical systems and semigroup theory.
The theory of substituion dynamical systems built from a single substituion has rapidly grown in the last decades and now, it is a mature subject where very important results have been achieved. The study of systems that mix several substitutions, however, is more difficult and even if strong results have already been obtained (for instance with the development of S-adic systems), a lot of research is to be done yet.
Given an alphabet of symbols, consider a finite set of substitutions of the alphabet and apply them, in some order, to get infinite sequences of substitutions. How does the behaviour of such sequences of substitutions relate to the semigroup generated by the substitutions? What can we say about the limit set of points obtained when those infinite substitution sequences are applied to the alphabet? How can we describe, in terms of the set of substitutions, the dynamical system obtained when a shift action is applied to the limit set of points? These are the kind of questions I am considering in my PhD project.
Furthermore, the collections of infinite sequences of symbols are, usually, rich in arithmetic and geometric structure, and they feet into a variety of other mathematical disciplines, including tilings, continued fractions theory or fractal geometry.
The study of single infinite sequences, in some cases, can also be of interest. In a joint work with Uwe Grimm, Yasushi Nagai and Petra Staynova, we have recently investigated arithmetic progressions within the Thue-Morse sequence and other related binary sequences (https://arxiv.org/abs/2101.02056).