## About me

Since November 2022, I am a maitre de conférence at université Paris-cité, at IRIF.

I defended my PhD thesis, *Étude homotopique des espaces stratifiés (Stratified homotopy theory)*, in July 2019, in Amiens. It was directed by David Chataur.

I then spent a year as an ATER in Amiens, from September 2019 to August 2020.

In October 2020, I received a grant from the FSMP, to stay as a post-doc at IRIF, Université de Paris, for a year.

From October 2021, to October 2022, I was a post-doc at Stockholm University.

I also was a student of École Normale Supérieure (Paris) between September 2012 and August 2016.

In 2021, I was awarded with the PhD prize from UPJV, amongst all people getting a PhD in science in the year 2019. You can find an elementary summary of my thesis here. It was written to be accessible to non-mathematicians (and even more accessible to non-specialists among mathematicians)

## Research interests

I am mainly interested in the homotopy theory of stratified spaces. This includes stratified homotopy theory itself, but also its applications to the study of classical invariants of stratified spaces, such as (generalised) intersection cohomology, or exit-paths (infinity)-categories. Moreover, I am interested in applications of stratified and homotopical techniques in other domains of mathematics, where stratifications appear as a way to encode certain structures (mainly in topology, but also in computer science, the latter is the motivation for my position at IRIF). Examples include: spaces with a group action, embeddings, or even operads.

## Publications

My PhD Thesis, in French, *Étude homotopique des espaces stratifiés,* (2019), ArXiV

Douteau, Sylvain, A simplicial approach to stratified homotopy theory. Trans. Amer. Math. Soc. (2021) ArXiV, journal

Douteau, Sylvain, Homotopy theory of stratified spaces. Algebr. Geom. Topol. (2021) ArXiV, journal

Douteau, Sylvain, Théorème de Whitehead stratifié et invariants de nœuds. C. R. Math. Acad. Sci. Paris (2019) ArXiV, journal

## Preprints

Douteau, Sylvain, A stratified Kan-Quillen equivalence (2021), ArXiV

Douteau, Sylvain and Waas, Lukas, From homotopy links to stratified homotopy theories (2021), ArXiV

Douteau,Sylvain and Labeye, Marie, Topologies et Distances sur les espaces de Ran, Draft version, in French

## Contact

You can contact me at sylvain.douteau at gmail.com