Algebraic Geometry
Members of the Research Group
- Ugo Bruzzo
- Barbara Fantechi
- Hua-Liang Chang
- Donatella Iacono
- Fabio Nironi
- Claudio L. S. Rava
- Alberto Celotto
- Fabio Ferrari Ruffino
Abdelmoubine Amar Henni
- Cristina Manolache
- Nicola Pagani
- Yao Yuan
Main External Collaborators
- Claudio Bartocci (Genova)
(Trieste)
- F. Fucito (Rome)
- Lothar Göttsche (ICTP Trieste)
- Daniel Hernandez Ruiperez (Salamanca)
- Le Dung Trang (ICTP, Trieste)
- Mudumbai Seshachalu Narasimhan (ICTP Trieste)
- Ramadas Ramakrishnan Trivandrum (ICTP Trieste)
- Vladimir Rittenberg (Bonn)
Main Research lines
- Construction of virtual classes and their use to define enumerative
invariants; properties of the invariants and methods for their
computations. Study of the enumerative significance.
- Extension to orbifolds/smooth Deligne-Mumford algebraic stacks of
constructions for manifolds, in particular Gromov-Witten invariants
and Chen-Ruan cohomology.
- Moduli spaces, such as moduli of sheaves, stable maps, varieties and
Hilbert and Quot schemes. Their infinitesimal study (i.e., deformation
theory) and additional structures such as algebraic stacks and
dg-schemes.
- Equivalences of derived categories of coherent sheaves and Fourier-Mukai transforms.
- Equivariant cohomology and localization in the noncommutative setting.
- Moduli spaces of Higgs bundles and of instantons. Applications to
topological field theories.
In all the above cases, particular attention is given to physically significant questions.