Research

Research interest

I work on analytic spaces over non-Archimedean fields. Such spaces can be seen as rigid spaces, as defined by Tate in the 70's. Later V. Berkovich gave a new viewpoint on the subject, introducing so-called k-analytic spaces. In the same way, R. Huber introduced adic spaces which gives another treatment of non-Archimedean analytic geometry. I try to work with all these theories, though I have mainly studied Berkovich's formalism.
Inside the world of non-Archimedean analytic geometry, my goal is to develop a theory of constructible sheaves which would be stable under as many operations as possible. This lead me to study non-Archimedean subanalytic sets, in particular the work of L. Lipshitz, and also to do some model theory (of algebraically closed valued fields).

Publications

Preprints

Other docments (Master's thesis, notes of lectures and expository works).

  • Connexité de certains espaces de Berkovich, my master's thesis in mathematics, under the supervision of Antoine Ducros (then at Nice Sophia-Antipolis University).
  • Channel machines, my master's thesis in computer science, under the supersvision of James Worrell (Oxford University, department of computer science).
  • Tameness for connected components of some subsets of Berkovich spaces A text where I prove that subanalytic sets in Berkovich spaces have finitely many connected components.
  • An introduction to adic spaces.
  • Some notes containing some remarks that I wrote while reading the article Continuous Valuations of Roland Huber.
  • Some notes of a mini course on Berkovich spaces for a Student Workshop (Regensburg, August 2015).
  • Some notes of a talk given in Regensburg for the course Linear groups and heights (by Walter Gubler and Clara Löh). It details a model theoretic argument of Emmanual Breuillard explaining that the Uniform Tits Alternative can be reduced to number fileds.
  • A note where I prove that a complex analogue of the Tarski-Seidenberg theorem about real semi-algebraic sets does not hold.