Salta gli elementi di navigazione
banner
logo ridotto
logo-salomone
DIMAI Dipartimento di Matematica e Informatica 'Ulisse Dini'

Geometria

Research topics

 

Algebraic geometry

Dolcetti, Maggesi, Ottaviani, Paoletti, Pertici, Rubei, Verdi, 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
  • Moduli spaces of vector bundles
  • Group actions on varieties and on tensor spaces
  • Geometry of tensors, Decomposition of tensors, Real and complex ranks of tensors
  • Spectral Theory of Tensors
  • Identifiability of Tensors
  • Canonical factorizations of matrices, Determinantal varieties, Secant varieties
  • 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, Sarfatti, Stoppato, Vlacci

 

  • 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
  • Slice-regular functions over quaternions
  • Quaternionic manifolds
  • Computer formalization for Complex and Hypercomplex Analysis

 

Complex, Symplectic, and Differential geometry

Angella, Battaglia, Calamai, Gentili, Nannicini, Patrizio, Podestà, Prato, Sarfatti, 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
  • Symplectic and complex toric geometry; orbifolds, quasifolds and stratified spaces associated to convex polytopes
  • 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

Rubei

 

  • Matrix completion

 

Foundations, didactic, popularization in Geometry

Battaglia, Conti, Dolcetti, Paoletti, Pertici, Verdi

 

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

 

Faculty staff

 

 

Postdocs

 

  • Alberto Raffero

 

PhD students

 

 

Other frequent collaborators

 

  • Elena Angelini
  • Alessandra Bernardi
  • Cristiano Bocci
  • Chiara Brambilla
  • Luca Chiantini
  • Juan Pablo Diaz Gonzalez
  • Jan Draisma
  • Benjamin Hennion
  • JM Landsberg
  • Valerio Melani
  • Massimilano Mella
  • Luke Oeding
  • Mauro Porta
  • Jasna Prezelj
  • Marco Robalo
  • Bernd Sturmfels
  • Alicia Tocino
  • Bertrand Toen
  • Nick Vannieuwenhoven
  • Alberto Verjovsky Sola

 

Visitors

 

 

Grants and projects

 

 

Seminars

 

 

PhD Courses

 
ultimo aggiornamento: 11-Ago-2017
Unifi Home Page

Inizio pagina