Algebraic Geometry and Number Theory

Research interests

  • Birational geometry, classification of algebraic varieties and of their degenerations.
  • Minimal model program.
  • Algebraic curves, their families and their moduli.
  • Jacobians, abelian varieties.
  • Geometry of the embeddings in projective spaces.
  • Algebraic surfaces and their moduli.
  • Moduli spaces of vector bundles on curves.
  • Moduli spaces of sheaves on K3 surfaces.
  • Hyperkaehler manifolds.
  • Holomorphic dynamics, residues, hyperbolicity.
  • Elliptic curve cryptography and post-quantum cryptography, isogeny based cryptography and isogeny graphs
  • Abelian varieties over number fields.
  • Algebraic curves over finite fields.
  • Arithmetic properties of algebraic varieties.
  • Arakelov class groups.
  • Group schemes.