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Mr Ibai Aedo

Profile summary

  • Research Student
  • Research Student
  • Faculty of Science, Technology, Engineering & Mathematics
  • School of Mathematics & Statistics
  • ibai.aedo

Professional biography

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 Learning 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 [1]. In 2019, I joined the School of Mathematics and Statistics at the Open University, where I am a member of the Aperiodic Order Research Group as well as the Dynamical Systems Seminar. I am pursuing a PhD under the supervision of Prof. Uwe Grimm†, Dr. Ian Short, Dr. Neil Mañibo and Dr. Reem Yassawi.

[1] I. Aedo Ibai and L. Lamata. Analog quantum simulation of generalized Dicke models in trapped ions. Phys. Rev. A, 97 (2018). https://doi.org/10.1103/PhysRevA.97.042317, https://arxiv.org/abs/1802.01853.

Research interests

My mathematical research interests lie, mainly, in symbolic dynamical systems and aperiodic order, together with the application of semigroup theory to the aforementioned fields.

I am currently involved in two research projects briefly described in the following two paraghraphs, one about forward limit sets of semigroups of substitutions and the other about monochromatic arithmetic progressions in automatic sequences.

Forward limit sets of substitution semigroups

In symbolic dynamical systems, alphabet substitutions play a central role. In particular, limit points of individual substitutions and S-adic directive sequences, as well as the dynamical systems arising from them under the shift action, have been thoroughly studied. With Ian Short, we investigate the semigroup generated by a given system of substitutions of an alphabet and its action on the set of words. More precisely, we study properties of the set of limit points obtained under the semigroup, called the forward limit set of the semigroup. We then apply the shift action to the forward limit set and study the resulting space, called the hull of the substitution system.

Monochromatic arithmetic progressions in automatic sequences

Inspired by van der Waarden's theorem stating that every colouring of the integers contains arbitrarily long monochromatic arithmetic progressions, with Uwe Grimm†, Yasushi Nagai and Petra Staynova, we have recently investigated monochromatic arithmetic progressions within the Thue-Morse sequence and other related binary sequences [2]. Neil Mañibo joined the group and we are now working on extending these results to automatic sequences in larger alphabets.

In addition to these projects, I am also interested in how substitution dynamical systems, which are usually rich in arithmetic and geometric structure, relate to a variety of other mathematical disciplines, including combinatorics, computer science, number theory, continued fractions theory and fractal geometry.

[2] I. Aedo, U. Grimm, Y. Nagai and P. Staynova. On long arithmetic progressions in binary Morse-like words. https://arxiv.org/abs/2101.02056.

Publications

Monochromatic Arithmetic Progressions in Binary Thue–Morse-Like Words (2022-10-23)
Aedo, Ibai; Grimm, Uwe; Nagai, Yasushi and Staynova, Petra
Theoretical Computer Science, 934 (pp. 65-80)

Analog quantum simulation of generalized Dicke models in trapped ions (2018)
Aedo, Ibai and Lamata, Lucas
Physical Review A, 97, Article 42317(4)