Loïs Faisant

IST Austria, Browning group.

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ISTA

Am Campus 1

3400 Klosterneuburg

Austria

Since December 2023, I am a postdoc researcher in mathematics, working as an IST-BRIDGE & Marie Skłodowska-Curie fellow in Tim Browning’s group, IST Austria.

Previously, I completed my PhD under the supervision of Emmanuel Peyre at Institut Fourier, Université Grenoble-Alpes.

mathematical interests

  • moduli spaces of curves
  • rational points/curves on varieties and variants such as Campana points/curves
  • \(p\)-adic/motivic integration, applications to arithmetics
  • birational geometry, applications to arithmetics

PhD thesis

My PhD project 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. I worked on a geometric analogue of the Batyrev-Manin-Peyre conjectures. The tools of motivic integration provide a nice framework to formulate this analogue; I studied, in a relevant ring of varities, the asymptotic behaviour of the class of the moduli space of curves of arbitrary large degree, for certain classes of varieties such as equivariant compactifications of groups or twisted products. My thesis also contains general predictions which are motivic analogues of the ones for rational points.

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


Ce projet doctoral était financé par une allocation ministérielle AMX.

contact

Courriel : lois dot my name at ista.ac.at


instances

J’ai occupé un siège de représentant élu des doctorant.e.s au Conseil du Collège des Études doctorales de l’UGA de début 2021 à fin 2022, et j’occupe actuellement un siège de suppléant à la Commission Recherche de l’UGA. Ne pas hésiter à me contacter à ce sujet.

Je recommande vivement la lecture de l’étude scientifique sur la précarité financière des doctorants à l’UGA commandée par le CED de l’UGA à une équipe des laboratoires Pacte et LaRAC. Un chiffre à retenir : “l’absence de financement a concerné chaque année en moyenne 14% des doctorant.es” sur la période 2017-2021.

news

Sep 1, 2023 In Fall 2023 I will be joining Browning’s group at IST Austria as an IST-BRIDGE fellow.
Jul 26, 2023 I successfuly defended my PhD thesis on July, 3rd.
Apr 6, 2023 In May I will give a talk at the Groups, Arithmetic & Algebraic Geometry Seminar at EPFL and attend the first meeting of the ERC ‘Groups of Algebraic Transformations’ in Rennes, France.
Feb 27, 2023 In March I will attend the first whorkshop of the ANR FRACASSO in Bordeaux, France.
Feb 16, 2023 My new preprint Motivic distribution of rational curves and twisted products of toric varieties is now available on the arXiv.

selected publications

  1. article
    Geometric Batyrev-Manin-Peyre for equivariant compactifications of additive groups
    Faisant, Loïs
    Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 2022
  2. preprint
    Motivic distribution of rational curves and twisted products of toric varieties
    Faisant, Loïs
    arXiv preprint 2023
  3. PhD thesis
    Stabilisation phenomena in moduli spaces of curves
    Faisant, Loïs
    Université Grenoble Alpes Summer 2023
  4. project
    High degree rational curves on blow-ups
    Faisant, Loïs
    2023