通信结构博士职位

PhD Position F/M Communication structures in tilings

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Contract type : Fixed-term contract

Level of qualifications required : Graduate degree or equivalent

Fonction : PhD Position

Context

This project will be carried out in the Inria team Mocqua, which focuses on emerging models of computation, in particular the interaction between discrete computations and continuous mathematics.

Assignment

Tilings are colorations of the plane submit to local constraints. We are looking for mathematical structures capturing the communication that is needed between cells to produce valid tilings respecting the given constraints. The goal will be to define such structures, study their properties and develop techniques to establish whether a given communication structure is able to generate tilings respecting a given set of constraints.

Main activities

The student will read the literature to get acquainted with the field of symbolic dynamics. He/she will study in details the recent articles about local generation of tilings and of languages [1,2,3,4]. There are several research directions. One of them is to improve the results developed in [1,2] by extending finite input alphabets to countably infinite ones, and establish whether the classification presented in [2] still holds under this relaxation. Most of the results in [1] apply to weakly mixing tilings: another direction is to understand what happens beyond this case, and to invent new techniques applicable with more generality. to identify the communication structures in graph colorings. In [4], it is shown that when the number of colors is sufficiently large, the graph itself suffices to generate is colorings, but we need to understand what happens for small numbers of colors.

[1] Favereau, Hoyrup. Local generation of tilings. Ergodic theory and dynamical systems. 45(11), 2025

[2] Favereau, Hoyrup. Local generation of tilings: the even bicolor Wang tilesets. Preprint, 2025

[3] Hoyrup. Local generation of languages. Preprint, 2026.

[4] Hoyrup. When a graph generates its own colorings. Preprint, 2026.

Skills

The student must have a background in mathematics or theoretical computer science, and should show interest in at least one of the following fields, which are at the heart of the project: symbolic dynamics, combinatorics, topology.

Benefits package

• Subsidized meals

• Partial reimbursement of public transport costs

• Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)

• Possibility of teleworking (after 6 months of employment) and flexible organization of working hours

• Professional equipment available (videoconferencing, loan of computer equipment, etc.)

• Social, cultural and sports events and activities

• Access to vocational training

• Social security coverage

Remuneration

€2300 gross/month

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General Information

• Theme/Domain : Proofs and Verification

• Town/city : Villers lès Nancy

• Inria Center :

Centre Inria de l'Université de Lorraine

• Starting date : 2026-10-01

• Duration of contract : 2 years, 11 months

• Deadline to apply : 2026-10-14

Warning : you must enter your e-mail address in order to save your application to Inria. Applications must be submitted online on the Inria website. Processing of applications sent from other channels is not guaranteed.

Instruction to apply

Defence Security :

This position is likely to be situated in a restricted area (ZRR), as defined in Decree No. 2011-1425 relating to the protection of national scientific and technical potential (PPST).Authorisation to enter an area is granted by the director of the unit, following a favourable Ministerial decision, as defined in the decree of 3 July 2012 relating to the PPST. An unfavourable Ministerial decision in respect of a position situated in a ZRR would result in the cancellation of the appointment.

Recruitment Policy :

As part of its diversity policy, all Inria positions are accessible to people with disabilities.

Contacts

• Inria Team :

MOCQUA

• PhD Supervisor :

Hoyrup Mathieu / mathieu.hoyrup@inria.fr

About Inria

Inria, the French national institute for research in digital science and technology, supports the French government in national research and innovation strategies in the digital field, acting as Digital Programs Agency. Inria leads over 300 research and innovation projects with its 3,500 scientists, engineers, and support staff, in partnership with universities and the digital ecosystem (businesses, entrepreneurs, and public stakeholders). Together, we explore strategic fields such as artificial intelligence, cybersecurity, quantum computing, cloud technologies, digital transformation in healthcare, digital twins, and digital technologies for defence. We develop practical solutions such as software, tech startups, partnerships with national companies, and cutting-edge training programmes. Our goal is to drive scientific, technological, and industrial excellence to ensure France’s digital sovereignty.