Ricerca Settori DisciplinariGeometria

Geometria

Faculty staff

Post-docs

Nicholas Lindsay
Hugo Pourcelot
Joshua Windare Oluwagbenga
Alexis Pierre Garcia

PhD Students

Francesco Iacca
Corrado Mazzoccoli
Lorenzo Mucciante
Lapo Rubini
Mirko Torresani
Federico Thiella

Research topics

Algebraic geometry

Derived geometry
DG-categories, Non-Commutative geometry, and applications to Arithmetic geometry, (Vanishing cycles, Singularity Theory, Bloch conductor conjecture)
Flag and loop Grassmannians for algebraic surfaces
K-theory for higher categories
Representation theory of algebraic groups
Fundamental groups
Algebraic stacks
Moduli spaces of vector bundles
Group actions on varieties and on tensor spaces
Geometry and identifiability of tensors
Canonical decompositions of matrices with coefficients in a field, and applications
Varieties of matrices: differential and algebraic properties
Logarithms of real matrices
Algebraic surfaces
Syzygies of varieties
LCI Algebraic Cycles
Set theoretic complete intersection, Ideal theoretic complete intersection
Geometric Complexity Theory
Algebraic Statistics
Computer formalization for Algebra and Geometry; Homotopy Type theory and Univalent Foundation
Shifted Poisson structures on affine Grassmannians

People: Dolcetti, Maggesi, Melani, Ottaviani, Paoletti, Pertici, Rubei, Vezzosi.

Some external collaborators: Benjamin Hennion, Andrea Maffei, Pavel Safronov, Bertrand Toën.

Complex and hypercomplex analysis

Geometric theory of holomorphic functions
Spaces of holomorphic functions
Monge-Ampère foliations and pluri-potential theory
Holomorphic dynamics
Automorphism groups and geometry of domains and complex manifolds, invariant metrics
Hyperbolic geometry
Modular forms
Complex and hypercomplex analysis and geometry, with applications
Slice-regular functions
Quaternionic manifolds
Orthogonal complex structures
CAGD applications
Computer formalization for Complex and Hypercomplex Analysis

People: Gentili, Maggesi, Patrizio, Stoppato.

Complex, symplectic and differential geometry

Riemannian and pseudo-Riemannian geometry, Riemannian manifolds with prescribed sectional curvature
Einstein metrics, Ricci solitons, Ricci flow with symmetries
Homogeneous spaces, complex homogeneous spaces, and invariant structures on homogeneous spaces
Norden and para-Norden geometry
Complex and symplectic geometry, Generalized-complex geometries, Non-Kaehler geometry
Complex Finsler Geometry
Cohomology of complex manifolds, Hodge theory
Special Hermitian metrics
Riemannian geometry of space of Kaehler metrics
Lagrangian foliations
Convex geometry and toric Kaehler geometry
Orbifold and quasifold structures, toric stratifications
Holomorphic foliations, LVMB manifolds
Complex structures in dimension 4
Twistor methods
Calibrated geometries
Quaternionic manifolds
Applications to Differential Geometry and to Computer Aided Geometric Design

People: Angella, Battaglia, Calamai, Gentili, Patrizio, Pediconi, Podestà, Prato, Stoppato, Verdiani.

Some external collaborators and former members: Adrián Andrada, Giuseppe Barbaro, Giovanni Bazzoni, Filippo Fagioli, Giovanni Gentili, Vincent Guedj, Anusha M. Krishnan, Chinh H. Lu, Liviu Ornea, Antonio Otal, Alexandra Otiman, Maurizio Parton, Giovanni Placini, Cristiano Spotti, Jonas Stelzig, Nicoletta Tardini, Adriano Tomassini, Luis Ugarte, Raquel Villacampa, Victor Vuletescu, Masoumeh Zarei, Michela Zedda.

Combinatorics

Weighted graphs

People: Calamai, Rubei.

Linear and multilinear algebra

Matrix completion
Decomposition of tensors, Real and complex ranks of tensors
Spectral Theory of Tensors
Identifiability of Tensors
Canonical factorizations of matrices, Determinantal varieties, Secant varieties
Maximal dimension of affine subspaces of matrices with certain characteristics

People: Ottaviani, Rubei.

Foundations, didactic, popularization in geometry

Didactic aspects of Mathematics and popularization
Mathematics, Music, and Architecture

People: Battaglia, Dolcetti, Paoletti, Pertici.

Seminars

Geometry at DIMAI Events

Ultimo aggiornamento

16.04.2025