Research

My current research revolves around non-archimedean geometry, tropical geometry, and Galois theory, with a special focus on the arithmetic of curves, abelian varieties, and their moduli spaces.

More broadly, I am interested in a variety of topics where algebra, arithmetic, and geometry come together in surprising ways, and in how to apply these to other branches of science. Lately, I have been thinking about computational algebraic geometry, topological data analysis, and algebraic statistics.

A statement of research interests (a bit outdated) is available here.

Publications and Preprints

• Weil representation and metaplectic groups over an integral domain (with Gianmarco Chinello), Comm. Alg. 43 (2015), no.6, 2388-2419.(arXiv). Here you find an addendum, where we treat the case of local fields of residual characteristic 2
• Galois descent of semi-affinoid spaces (with Lorenzo Fantini), Math. Z. (2018) vol. 290: 1085-1114 (arXiv).
• Berkovich curves and Schottky uniformization I: The Berkovich affine line (with Jérôme Poineau) in Arithmetic and Geometry over Local Fields, Springer Lecture Notes in Mathematics 2275 (2021).
• Berkovich curves and Schottky uniformization II: analytic uniformization of Mumford curves (with Jérôme Poineau) in Arithmetic and Geometry over Local Fields, Springer Lecture Notes in Mathematics 2275 (2021).
• Triangulations of Berkovich curves and ramification (with Lorenzo Fantini). To appear in the Annales de l’Institut Fourier (2021). (arXiv) 
• Stabilization indices of potentially Mumford curves (with Andrew Obus). (arXiv)
• Hurwitz graphs and Berkovich curves. (Preprint).
• Equidistant liftings of elementary abelian Galois covers of curves (Preprint).
• Schottky spaces and universal Mumford curves over Z (with Jérôme Poineau). (Preprint)

Other Writings

- Buissons et Balais: la forme des espaces analytiques non-Archimédiens (in French), Images des Mathématiques, CNRS, 2013.
- Dans les coulisses du MoMath (in French), Images des Mathématiques, CNRS, 2019.
- Contributions to Arithmetic Geometry in Mixed Characteristic, my PhD thesis.
- The slides of some of my talks.