Research

My research has been roaming in the fields of algebraic geometry and number theory for some time, stopping by scenic spots such as the arithmetic of curves, non-archimedean geometry and moduli spaces. I still work on these topics, but I have now expanded my interests to include pedagogical aspects, such as how to assimilate mathematical notions effectively and how to convey the beauty and power of mathematics to a general public through outreach and public engagement.

I am also enjoying discovering applications of algebraic geometry to other branches of science and how machine learning can be leveraged to obtain examples and conjectures in mathematics. I am a member of the applied algebra and geometry network with particular interests in computational algebraic geometry, techniques from machine learning and data science, and algebraic statistics.

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). [arXiv link to an (unrefereed) preprint containing most of the content of the two surveys above.]
• Triangulations of Berkovich curves and ramification (with Lorenzo Fantini). Annales de l'Institut Fourier (2022). [arXiv]  
• Schottky spaces and universal Mumford curves over Z (with Jérôme Poineau). Sel. Math. New Ser. 28, 79 (2022). [arXiv]
• Stabilization indices of potentially Mumford curves (with Andrew Obus). [arXiv]
• On the arithmetic and geometry of spaces L_m+1,n (With Michel Matignon and Guillaume Pagot). [arXiv]
• Hurwitz graphs and Berkovich curves. [Preprint]
• Equidistant liftings of elementary abelian Galois covers of curves. [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.
- Lecture notes for a FIM minicourse at ETH - Zürich
- The slides of some of my talks.