Research group in algebraic geometry and related areas

Academic staff
Enrico ArbarelloRuggero Bandiera, Simone DiverioDomenico Fiorenza, Marco Manetti, Gabriele Mondello, Kieran O'Grady, Riccardo Salvati Manni

Post-docs and graduate students
Francesco Meazzini,

Research areas

  • Deformation theory (Fiorenza, Manetti, Meazzini). Deformations of complex manifolds and holomorphic maps, homotopical methods in deformation theory, differential graded Lie algebras, L-infinity algebras.
  • Modular varieties (Salvati Manni) Moduli spaces of abelian varieties, modular varieties, Borcherds products, theta functions, modular forms.
  • Riemann surfaces (Arbarello, Mondello). Hyperbolic surfaces, geometric structures on Riemann surfaces, Teichmüller theory, moduli spaces of curves,representations of surface groups, Higgs bundles.
  • Chow groups  (O'Grady): Chow rings of smooth projective varieties, Bloch-Beilinson conjectures.
  • Hyperkaehler varieties (Arbarello, O'Grady). Projective geometry of hyperkaehler varieties. Moduli and periods. Deformation types.
  • Higher structures in algebra and geometry (Manetti, Meazzini) Homotopy and cohomology theory of L-infinity algebras, derived brackets, formality criteria.
  • Complex analytic, algebraic, and differential geometry (Diverio) Kobayashi hyperbolicity theory, positivity in complex algebraic geometry, special and extremal metrics on compact Kähler manifolds.

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