I am broadly interested in birational geometry, moduli theory and singularity theory of algebraic varieties. Currently I am mainly thinking about varieties in positive characteristic: already for surfaces there are several deep and unsolved questions related to singularites and moduli theory.
You can find my arXiv profile page here, where pdf's of the following articles are available.
Equisingular lifting of semi-log canonical F-split K-trivial surfaces, with F. Bernasconi. Available on the ArXiv.
Pathological MMP singularities as $\alpha_p$-quotients. Available on the ArXiv.
Resolution of 1-foliations singularities on surfaces and threefolds. Available on the arXiv.
On the singularities of quotients by 1-foliations. To appear in Nagoya Math. Journal. Available on the arXiv.
Normality of minimal log canonical centers of threefolds in mixed and positive characteristic, with E. Arvidsson. To appear in Ann. Inst. Fourier (Grenoble).
Abundance for slc surfaces over arbitrary fields. EPIGA, Volume 7, Article No. 5, 2023.
Gluing for stable families of surfaces in mixed characteristic. Algebraic Geometry 12, No. 2, 2025.
Gluing theory for slc surfaces and threefolds in positive characteristic. Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 25, No.2, 2024.
Posivity of the CM line bundle for K-stable log Fanos. Trans. Am. Math. Soc. 375, No. 7, 2022.
My PhD thesis, titled On the Projectivity of some moduli spaces of varieties, is formed by my first four articles. It is available upon personal request. Amongst the 2022 EPFL PhD theses, it was awarded the Mathematics Doctoral Thesis Award, and received an EPFL Program Thesis Distinction.
Below are some notes I took during mini-courses at various occasions, indicated in brackets.
Perfectoïds and singularities in mixed characteristic (L. Ma, May 2023, Ann Arbor)
Local and global applications of perfectoïds (K. Schwede, May 2023, Ann Arbor)
Introduction to non-archimedian geometry (K. Hübner, March 2024, Heidelberg)
Resolution of complex foliations (A. Belotto, March 2024, Heidelberg)
Old and new techniques in resolution of singularities (M.H. Quek, March 2024, Heidelberg)
Some short research notes:
Here are some various notes I wrote during my PhD. I claim no originality, and all the mistakes are obviously mine.
Cohomologie cristalline (pdf, in French). Detailed notes for a seminar on Crystalline Cohomology held at EPFL in Spring 2022. Written in French, unfinished for now.
A general presentation of moduli theory of algebraic varieties, aimed at mathematical PhDs and post-docs (pdf, in English).
Duality on Normal varieties (pdf, in English). The Serre duality explained in Hartshorne's book (III.7) can be extended to normal projective varieties. The proof is a simple application of the properties of reflexive sheaves, and many details are spelled out.
Cones (pdf, in English). Some basic results on affine, projective and relative cones.
Some notes about divisors (pdf, in English). Basics about pullback of divisors, intersection of Cartier divisors, divisors on Fano varieties and adjunction theory.