Ricerca Settori DisciplinariGeometria
Geometria
Research topics
Algebraic geometry
Dolcetti, Maggesi, Melani, Ottaviani, Paoletti, Pertici, Rubei, Vezzosi
- Derived geometry
- DG-categories, Non-Commutative geometry, and applications to Arithmetic geometry, (Vanishing cycles, Singularity Theory, Bloch conductor conjecture)
- Geometric Langlands for 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
Complex and hypercomplex analysis
Gentili, Maggesi, Patrizio, Stoppato
- 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
Complex, Symplectic, and Differential geometry
Angella, Battaglia, Calamai, Gentili, Patrizio, Pediconi, Podestà, Prato, Stoppato, Verdiani
- 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
Combinatorics
Calamai, Rubei
Linear and multilinear algebra
Ottaviani, Rubei
- 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
Foundations, didactic, popularization in Geometry
Battaglia, Dolcetti, Paoletti, Pertici
- Didactic aspects of Mathematics and popularization
- Mathematics, Music, and Architecture
Faculty staff
Postdocs
- Filippo Fagioli
- Cosimo Flavi
- Giovanni Gentili
- Giovanni Placini
PhD students
- Giuseppe Barbaro
- Ettore Teixeira Turatti
Other frequent collaborators
- Elena Angelini
- Alessandra Bernardi
- Cristiano Bocci
- Chiara Brambilla
- Luca Chiantini
- Juan Pablo Diaz Gonzalez
- Jan Draisma
- Benjamin Hennion
- JM Landsberg
- Massimilano Mella
- Antonella Nannicini
- Luke Oeding
- Alexandra Otiman
- Francesco Panelli
- Mauro Porta
- Jasna Prezelj
- Alberto Raffero
- Marco Robalo
- Giulia Sarfatti
- Bernd Sturmfels
- Nicoletta Tardini
- Alicia Tocino
- Bertrand Toen
- Nick Vannieuwenhoven
- Alberto Verjovsky Sola
- Luisella Verdi
- Fabio Vlacci