Biography
Florian Viguier
Doctor in mathematics
University of Strasbourg
University of Strasbourg
Current situation
I conducted my PhD thesis under the supervision of Christine Huyghe on the subject of Fourier-Mukai transforms for algebraic differential operators over a formal abelian variety. I defended it on December 16, 2021 at the IRMA of Strasbourg.
Scientific mediation
In parallel of my research and teaching, I also dedicate myself to the scientific mediation via various events. Here are a few that I'm taking at heart:
Parcours Énig'maths: This is a mathematical puzzle course I co-organize. It is held every fall during the Strasbourg 'Fête des sciences' and brings together dozens of people of all ages around the pleasure of solving enigmas. Some of these will be uploaded on the 'Enigmas' section of my website.
Math en Jeans: These are research workshops in middle or high school supervised by university researcher. The goal is to give young people a preview of what the research in mathematics is. You can find some subjects from previous years here (in French).
Research topic
Key words: Abelian varieties, arithmetic D-modules, cristalline D-modules, Fourier-Mukai transform, rigid analytic varieties.
In 1981, Shigeru Mukaï defined the now called Fourier-Mukaï transform for abelian varieties over algebraically closed fields, which gives an equivalence of categories between quasi-coherent sheaves over an abelian variety and quasi-coherent sheaves over its dual. It has some important applications in other domains such as mirror symmetry and string theory.
Thanks to the independent work of Laumon and Rothstein, the construction of the Fourier-Mukaï transform have been extended to sheaves of differential operators on a locally noetherian base of characteristic zero, using the universal vectorial extension of the dual of an abelian variety.
The goal of my research is to define similar transforms in the arithmetic case, using the arithmetic sheaves of differential operators introduced by Berthelot. This induces, among others, a deep comprehension of the Poincaré sheaf and the construction of an arithmetic group scheme analogous to the universal vectorial extension of the dual abelian variety.