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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

 

  • Weighted graphs

 

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

  • Cosimo Flavi
  • Giovanni Gentili
  • Hugo Pourcelot

PhD students

  • Lapo Rubini
  • Federico Thiella

Other frequent collaborators

  • Elena Angelini
  • Giuseppe Barbaro
  • Alessandra Bernardi
  • Cristiano Bocci
  • Chiara Brambilla
  • Luca Chiantini
  • Juan Pablo Diaz Gonzalez
  • Jan Draisma
  • Filippo Fagioli
  • Benjamin Hennion
  • JM Landsberg
  • Massimilano Mella
  • Antonella Nannicini
  • Luke Oeding
  • Alexandra Otiman
  • Francesco Panelli
  • Giovanni Placini
  • Mauro Porta
  • Jasna Prezelj
  • Alberto Raffero
  • Marco Robalo
  • Giulia Sarfatti
  • Bernd Sturmfels
  • Nicoletta Tardini
  • Ettore Teixeira Turatti
  • Alicia Tocino
  • Bertrand Toen
  • Nick Vannieuwenhoven
  • Alberto Verjovsky Sola
  • Luisella Verdi
  • Fabio Vlacci

Grants and projects

Seminars

PhD Courses

Mailing lists

Ultimo aggiornamento

06.11.2023

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