I am a "maître de conferences", which could roughly be translated as "conference master", in the logic team of the lacl.
I did my thesis with Andrzej Zuk
at the Paris-Cité university. My first post-doc was in Saarbrücken, under the guidance of
Laurent Bartholdi.
Finally, between September
2023 and August 2025, I was a von Humboldt fellow working with
Vasco Brattka in Munich.
Research
I mainly work at the intersection of computability theory and group theory.The study of decision problems for finitely generated groups has led me to study computable analysis, because it is in this domain that a robust framework for studying computability in mathematics was developed: the notions of represented space, problems as multi-valued functions between represented spaces, Weihrauch reducibility (which is the correct definition of many-one reducibility, and which can be used to give a robust notion of Turing reducibility via the diamond operator on the Weihrauch lattice).
In many cases, when studying computability in mathematics, one does not need the full power of the theory of representations, and one can get away with using non-general notions. However, in the settings that I consider, the presence of topological spaces which naturally contain undecidability makes the use of the theory of representations necessary.
An illustrative example of the above point arises in the study of the space of marked groups: the space of marked groups is a Polish space, but it is not computably Polish because it is not computably separable. Because of this, the approach to effective descriptive set theory based on notions of computable presentations cannot be applied to the space of marked groups.
I am also very interested in the differences between Type 1 and Type 2 computability, and in the continuity problem for Markov computable functions.
Publications
- Join appendix to an article of Arman Darbinyan: A robust family of residually finite groups; spectra of residual finiteness growth, computability properties, and other applications (with an appendix by Arman Darbinyan and Emmanuel Rauzy), Preprint, 2025.
- With Vasco Brattka. Effective Second Countability in Computable Analysis, full version (submitted), conference version, CiE 2025.
- With Laurent Bartholdi and Leon Pernak. Groups with presentations in EDT0L. Groups, Geometry and Dynamics, 2025. Here is a recorded talk.
- New definitions in the theory of Type 1 computable topological spaces. Accepted in Computability, 2023.
- Multi-representation associated to the numbering of a subbasis and formal inclusion relations. Logical Methods in Computer Science, 2025.
- A generalization of Markov's approach to the continuity problem for Type 1 computable functions. Preprint, 2023.
- Remark and problems about algorithmic descriptions of groups. International Journal of Algebra and Computation, 2025.
- Computable analysis on the space of marked groups. Preprint, 2021. Recorded talk.
- Computability of finite quotients of finitely generated groups. Journal of Group Theory, 2022.
- Obstruction to a Higman Embedding Theorem for residually finite groups with solvable word problem. Journal of Group Theory, 2021.
