Research interests

• Arithmetic geometry
• Model theory
• Automata Theory
• Computational complexity
• Machine learning

Publications

1. Differentiability of relative volumes over an arbitrary non-archimedean field with Sébastien Boucksom and Walter Gubler, International Mathematics Research Notices (IMRN), 2020.
2. Differentiability of non-archimedean volumes and non-archimedean Monge-Ampere equations with Jose Burgos, Walter Gubler, Philipp Jell, Klaus Künnemann and an appendix by Robert Lazarsfled, Algebraic Geometry (Foundation Compositio Mathematica), Volume 7, Issue 2 (March 2020).
3. On Zhang's semipositive metrics with Walter Gubler, Documenta Mathematica 24 (2019), 331--372.
4. Continuity of Plurisubharmonic Envelopes in Non-Archimedean Geometry and Test Ideals with Walter Gubler, Philipp Jell, Klaus Künnemann and an appendix by Jose Burgos and Martin Sombra, Annales de l'Institut Fourier, Volume 69 (2019) no. 5, p. 2331-2376.
5. Equations over free inverse monoids with idempotent variables (with Volker Dikert, Géraud Sénizergues and Pedro V. Silva), Theory of Computing Systems, volume 61, pages494–520 (2017).
6. A definable p-adic analogue of Kirszbraun's Theorem on extensions of Lipschitz maps (with Raf Cluckers) Journal of the Institute of Mathematics of Jussieu, Vol. 17, no. 1, 39 -- 57.
7. Analytic functions on tubes of non-Archimedean analytic spaces, with an appendix by Christian Kappen, Algebra and Number theory, 11 (2017), 657-683.
8. Overconvergent subanalytic subsets in the framework of Berkovich spaces, Journal of the European Mathematical Society, 18 (2016) n 10, 2405-2457.
9. Equations over free inverse monoids with idempotent variables (with Volker Dikert, Géraud Sénizergues and Pedro V. Silva) Lecture Notes in Computer Science, 9139 (2015), 173-188. This paper was awarded the Yandex best paper award at the CSR 2015 conference (International Computer Science Symposium in Russia).
10. A note on tropicalization in the context of Berkovich spaces, Israel Journal of Mathematics, 210 (2015) n. 1, 323-334.
11. Cohomology of locally closed semi-algebraic subsets, Manuscripta Mathematica (2014), Volume 144 (Issue 3-4), 373-400.
12. Constructibility in Berkovich spaces, Phd Thesis defended on October 7, 2013 at Pierre and Marie Curie University (Paris 6), under the supervision of Jean-François Dat and Antoine Ducros.
13. Cohomolgie étale des ensembles semi-algébriques dand les espaces de Berkovich, Proceedings of the 12th Forum des jeunes mathématicien-ne-s held at the IHP Paris (from 12-14 November 2012).

Preprints

• Non-Archimedean volumes of metrized nef line bundles with Sébastien Boucksom and Walter Gubler, arxiv 2011.06986.

Organization of conference

• I co-organized the Workshop Regensburg days on non-Archimedean geometry in July 2016 (poster of the conference).

Other works

• Dimension in non-Archimedean geometries, simplification of existing proofs as well as generalization of results about the dimension of non-Archimedean subanalytic sets, arxiv: 1401.6942.
• 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.

Talks in conferences and seminars

Here is a selected list of talks I gave

• Conference Berkovich spaces, at the Institut Henri Poincare in Paris, July 2018.
• Ergodic geometry seminar, Ecole Polytechnique, Paris, October 2016.
• Conference on Arakelov geometry, Regensburg, September 2016.
• Seminar of Arithmetic geometry, Essen University, January 2015.
• Model theory Seminar, MSRI Berkeley, February 2014.
• Arithmetic Geometry Seminar (organized by Pr. Peter Scholze), Bonn Germany, December 2012.