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Algebra and Geometry

About us

The scientific activities of the group traverse non-commutative algebra, combinatorics, representation theory, and various branches of geometry (algebraic, complex, differential, Kähler, projective, symplectic) often at the interface with mathematical physics.
Specific research interests include:

  • Ring and nearring theory
  • Infinite-dimensional Lie algebras
  • Hopf algebras and quantum groups
  • Integrable systems and homogeneous spaces
  • Kähler Geometry
  • Complex non-Kähler Geometry
  • Deformation of complex structures
  • Holomorphic dynamics
  • Semi-Riemannian geometry

The Geometry group is a member of PRIN 2022 - Real and Complex Manifolds: Geometry and Holomorphic Dynamics. The local unit is coordinated by Adriano Tomassini.


Andrea APPEL
Representation Theory and Mathematical Physics.
IRIS - Scopus

Anna (Miriam) BENINI
Holomorphic dynamics in one and several complex variables, especially concerning the iteration of transcendental maps.
IRIS - Scopus

Semi-Riemannian geometry; existence, uniqueness and molteplicty results of closed geodesics geometrically distinct. Genericity of nondegenerate critical points and bumpy metric theorem on Semi-Riemannian geometry.
Isometric actions on symmetric spaces of compact type and isometry actions of noncompact Lie group on compact Lorentazian manifold. Symplectic geometry, Hamiltonian actions and moment map.
IRIS - Scopus

Complex and Differential Geometry.
IRIS - Scopus

Costantino MEDORI
Special structures on differentiable manifolds (in particular Cauchy-Riemann and paracomplex structures) and homogeneous spaces.
IRIS - Scopus

Fiorenza MORINI
a) Theory of nearrings. Study of specific classes of nearrings: for example Orthodox nearrings, A-rigid nearrings and weakly divisible nearrings. Such nearrings have provided a starting point for further study aimed at geometric-combinatorial structures (for example in building designs and codes from weakly divisible nearrings).
b) Theory of groups. Asymptotic problems and probabilistic methods.
Topic of research is to study the function P_G (t) that expresses the probability that t elements taken at random from a group G generate the same group. The function P_G can be expressed as Dirichlet series, and then extended by interpolation to a complex-valued function, the inverse of that function is called probabilistic zeta function of the group G.
IRIS - Scopus

Differential geometry, especially the geometry of submanifolds in homogeneous spaces and the study of integrable systems, by the methods of exterior differential systems and of the moving frame.
IRIS - Scopus

My research is mainly in complex analysis, CR geometry and differential geometry.
More precisely, I have studied, under appropriate convex properties of domains in C^n (convexity, C-convexity, strictly and strongly pseudoconvexity): extension of functions and analytic objects; relation between the notion of Hilbert and Kobayashi hyperbolicity.
IRIS - Scopus

Nicoletta TARDINI
Complex and Differential Geometry.
IRIS - Scopus

1) Cohomological properties of almost complex manifolds;
2) Special metrics on complex manifolds;
3) D-complex structures;
4) Deformations of complex structures.
IRIS - Scopus

Michela ZEDDA
Kähler geometry (projectively induced metrics, balanced metrics,
Tian-Yau-Zelditch asymptotic expansion, Hermitian symmetric spaces).
Symplectic geometry (Global symplectic coordinates).
Complex non-Kähler and Sasakian geometry (Geometric flows, Sasakian manifolds, Strong Kähler with torsion structures).
IRIS - Scopus

Claudio AREZZO (on leave to ICTP)
1) Existence problem for special submanifolds of Einstein spaces.
2) Existence of special metrics on compact complex manifolds.
3) Analysis on manifolds and special metrics
4) Ricci flow on complex manifolds
IRIS - Scopus


Stefano MARINI
Complex geometry and Differential Geometry.
IRIS - Scopus

Riccardo PIOVANI
Complex geometry and Differential Geometry.
IRIS - Scopus

Graduate Students

Ciclo XXXVI. Tutor: M. Benini

Ciclo XXXVII. Advisor: M. Benini, A. Saracco

Ciclo XXXVII. Advisor: M. Zedda

Ciclo XXXIX. Tutor: C. Felisetti (Modena-Reggio Emilia) e M. Zedda

Victor Gustavo MAY CUSTODIO
Ciclo XXXIX. Tutor: L. Biliotti

Christian SOPIO
Ciclo XXXIX. Tutor: A. Saracco

National Research Projects

PRIN 2022 - Real and Complex Manifolds: Geometry and Holomorphic Dynamics (2022AP8HZ9)
Coordinatore Nazionale: F. Bracci (Università di Roma Tor Vergata). Coordinatore Locale Unità di Parma: A. Tomassini.
Start date: Sept. 28, 2023. End date: Sept. 27, 2025.

Pubblicato Mercoledì, 25 Giugno, 2014 - 11:48 | ultima modifica Venerdì, 10 Novembre, 2023 - 13:22

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