research

PhD thesis

My PhD project, conducted under the supervision of Emmanuel Peyre at Institut Fourier, Université Grenoble Alpes, from 2020 to 2023, concerned the study of stabilisation phenomena occuring in the moduli space of rational curves on a nice variety (typically, a Fano variety), or more generally the moduli space of sections of a nice family above a smooth projective irreducible curve.

In my PhD thesis, I formulate a geometric/motivic analogue of the Batyrev-Manin-Peyre conjectures unsing the tools of motivic integration. One asks about the asymptotic behaviour, in a well-chosen ring of varities, of the class of the moduli space of curves of arbitrary large degree. These predictions have to be understood as questions or principles concerning the distribution of curves on Fano-like varieties.

Then I verify the validity of these predictions for certain classes of varieties such as equivariant compactifications (vector spaces, split torus) or twisted products obtained from them.

This type of questions is still at the center of my research project.

Keywords: moduli space, rational curves, Fano varieties, motivic Euler product.

This project was supported by a doctoral grant awarded by l’École polytechnique to its former students. / Ce projet doctoral était financé par une allocation ministérielle AMX.

On-going projects

• Motivic couting of curves using universal torsors , in preparation.
• A Poisson formula for algebraic tori and applications to motivic zeta functions , joint work with M.Bilu, in preparation.
• Motivic delta method and diagonal forms, joint project with T.Browning.
• On triples of squareful polynomials over function fields in positive characteristic, joint work with A.Mirzaee, in preparation.
• Counting representations of quivers, joint project with T.Vernet.
• Motivic Eisenstein series and distribution of curves on flag varieties, joint project with M.Bilu.

additional material

my master 2 thesis (in French).