ALGEBRA AND GEOMETRY
Scientific Sectors
- SSD: Mat/02, Mat/03
- ERC: PE1_2 Algebra, PE1_3 Number theory, PE1_4 Algebraic and complex geometry, PE1_5 Geometry
Research Topics
- Computational methods for commutative algebra, with interactions with combinatorics and algebraic geometry.
- Categorical algebra, cohomology of non-abelian structures.
- Monoidal categories, monads, (semi)separable functors.
- Hopf algebras and their generalizations.
- Algebraic groups and representations.
- Arithmetic properties of automorphic forms.
- Higher dimensional complex projective varieties.
- Fano varieties, Mori theory, birational geometry & MMP, rational curves.
- Toric varieties and Mori dream spaces.
- Mirror symmetry and toric geometry.
- Deformation theory and moduli spaces.
- K3 surfaces, derived categories, Fourier-Mukai functors.
- Brauer groups and Picard stacks.
- Hurwitz spaces and monodromy of projective curves.
- Hilbert schemes and computational aspects.
- Complex and symplectic geometry.
- G-structures and special holonomy.
- Calibrated geometry.
- Geometric flows: Ricci flow, mean curvature flow, etc.
- Minimal surfaces.
- Conformal geometry.
- Submanifolds with prescribed (Riemannian/Lorentzian) mean curvature.
- Function theory on Riemannian manifolds.
- Lorentzian manifolds and mass related problems.