Motto:
"Let no one ignorant of geometry leave here", Shing-Tung Yau - The Shape of Inner Space.
Research interests
The Geometry group in Genova has research interests that include: Algebraic Geometry, Complex Geometry, Geometric Topology, Geometry from Mathematical Physics, Algebraic Number Theory, and Arithmetic Geometry. More specifically, some topics that are actively pursued by faculty members of this group are:
Geometry of complex algebraic surfaces, in particular k3 surfaces, surfaces of general type and their moduli spaces.
Geometry, constructions and moduli of higher dimensional varieties, also via computational methods, and in particular: irreducible symplectic manifolds, varieties of general type, Fano varieties, and abelian varieties.
The theory of abelian varieties, modular forms and their associated L-functions.
Birational geometry, Mori dream spaces, and the classification of algebraic varieties through the study of their contraction morphisms.
Moduli spaces of sheaves on complex surfaces; quiver varieties; Fourier-Mukai and Nahm transforms.
Geometry and topology of locally symmetric spaces; arithmetic properties of lattices.
Convex geometry of Newton-Okounkov bodies together with its relation to positivity aspects in algebraic geometry and the study of syzygies of algebraic varieties.
Geometry of integrable systems; bi-Hamiltonian structures; special-Kähler geometry.
Geometry and applications to gauge theory and to string theories.
History of mathematics in the 19th and 20th centuries; philosophical aspects of the relationship between geometry and physics.
