## 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