I work on mirror symmetry, non-archimedean geometry and tropical geometry.
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.
- Secondary fan, theta functions and moduli of Calabi-Yau pairs, joint with P. Hacking and S. Keel, (arXiv:2008.02299), 2020.
- Non-archimedean quantum K-invariants, joint with M. Porta, (arXiv:2001.05515), 2020.
- The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus, joint with S. Keel, (arXiv:1908.09861), 2019.
- The non-archimedean SYZ fibration, joint with J. Nicaise and Chenyang Xu, Compositio Mathematica, 155(5):953–972, 2019.
- Derived Hom spaces in rigid analytic geometry, joint with M. Porta, (arXiv:1801.07730), To appear in Publications of the Research Institute for Mathematical Sciences, Special issue dedicated
to Professor Masaki Kashiwara on his seventieth birthday, 2018.
- Representability theorem in derived analytic geometry, joint with M. Porta, (arXiv:1704.01683), To appear in Journal of the European Mathematical Society, 2017.
- Enumeration of holomorphic cylinders in log Calabi-Yau surfaces. II. Positivity, integrality and the gluing formula, (arXiv:1608.07651), To appear in Geometry & Topology, 2016.
- Derived non-archimedean analytic spaces, joint with M. Porta, Selecta Mathematica, 24(2):609–665, 2018.
- Enumeration of holomorphic cylinders in log Calabi-Yau surfaces. I, Mathematische Annalen, 366(3):1649-1675, 2016.
- Higher analytic stacks and GAGA theorems, joint with M. Porta, 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, Journal für die reine und angewandte Mathematik (Crelle), 741:179–210, 2018.
- 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.