## About me

I am a von Humboldt fellow working in Munich with Vasco Brattka.

Last year, 2022-2023, I was a post-doc at Saarland university working with Laurent Bartholdi. And before that, I was a PhD student working under the supervision of Andrzej Zuk.

### Research interests

I work at the intersection of computability theory and of group theory.

In the study of infinite countable groups, many unsolvable algorithmic problems arise naturally, and computability turns out to be a very good tool to classify the complexity of different classes of groups: some classes are recursively enumerable, while others are not, some have solvable isomorphism problem, while others don’t, and so on.

I also work with the theory of numberings, which uses computability to build a theory of finite descriptions of infinite objects. In particular I have worked on the notion of "Type 1 computable topological space", the notion of computable topological space that we obtain by working with numberings.

## Articles

With Laurent Bartholdi and Leon Pernak. Groups with presentations in EDT0L. Preprint, 2024

New definitions in the theory of Type 1 computable topological spaces. Preprint, 2023. Slides.

Multi-representation associated to the numbering of a subbasis and formal inclusion relations. Preprint, 2023

A generalization of Markov's approach to the continuity problem for Type 1 computable functions . Preprint, 2023

Remarks and problems about algorithmic descriptions of groups. Preprint, 2021

Computable analysis on the space of marked groups. Preprint, 2021

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

email: emmanuel.rauzy.14 at normalesup dot org

### Some recorded talks

Présentations de groupes dans EDT0L (exposé en français)

Groups with presentations in EDT0L

Computability on the space of marked groups