Geometry
Geometry of tensors and its applications. Differential geometry applied to computer vision.
Fiber bundles in the complex projective spaces.
Cohomology of locally Cohen-Macaulay complex projective curves.
Algebraic geometry. In particular: classification of projective varieties of small dimension.
Projective varieties covered by linear spaces. Linear systems of matrices of constant rank.
Differential-geometric properties of algebraic varieties.
In algebraic geometry, with particular interest in the geometry, topology and automorphisms
of complex algebraic varieties and orbifolds; moduli spaces and stacks.
My research field is the geometric topology of low-dimensional manifolds.
As main tools, I use branched coverings, Kirby diagrams, and Lefschetz fibrations.
- Gonality of algebraic curves
- Computational algebraic geometry of cubic surfaces
- Convex geometry
- Moduli spaces of curves
- Topological recursion
- Integrable hierarchies
- Resurgence