I work on non-archimedean geometry, tropical geometry and mirror symmetry.
I aim to build a theory of enumerative geometry in the setting of Berkovich spaces, which I call non-archimedean enumerative geometry.
The theory will give us a new understanding of curve counting in Calabi-Yau manifolds, as well as the structure of their mirrors.
It is also intimately related to the theory of cluster algebras and wall-crossing structures.
I am awarded the Clay Research Fellowship in 2016.
Papers: (BibTeX entries)
- (with Nicaise and Xu) The non-archimedean SYZ fibration, (arXiv:1802.00287), To appear in Compositio Mathematica.
- (with Porta) Derived Hom spaces in rigid analytic geometry, (arXiv:1801.07730).
- (with Porta) Representability theorem in derived analytic geometry, (arXiv:1704.01683), To appear in Journal of the European Mathematical Society.
- Enumeration of holomorphic cylinders in log Calabi-Yau surfaces. II. Positivity, integrality and the gluing formula, (arXiv:1608.07651).
- (with Porta) Derived non-archimedean analytic spaces, (arXiv:1601.00859), To appear in Selecta Mathematica.
- Enumeration of holomorphic cylinders in log Calabi-Yau surfaces. I, Mathematische Annalen, 366(3):1649-1675, 2016.
- (with Porta) Higher analytic stacks and GAGA theorems, Advances in Mathematics, 302:351–409, 2016.
- Tropicalization of the moduli space of stable maps, Mathematische Zeitschrift, 281(3):1035–1059, 2015.
- Gromov compactness in non-archimedean analytic geometry, (arXiv:1401.6452), To appear in Journal für die reine und angewandte Mathematik (Crelle).
- The number of vertices of a tropical curve is bounded by its area, L’Enseignement Mathématique, 60(3-4):257–271, 2014.
- Balancing conditions in global tropical geometry, Annales de l'Institut Fourier, 65(4):1647–1667, 2015.
My thesis: Premiers pas de la géométrie énumérative non archimédienne, defended in December 2015.