Research

Research interests

• slice regular functions over the quaternions: geometric theory, quaternionic Hardy spaces, Hankel operators, Carleson measures;
• quaternionic geometry : quaternionic regular manifolds, quaternionic toric manifolds;
• analytic function spaces: Dirchlet space on the complex bidisc, Carleson measures, relation with potential theory in the discrete setting;
• hyperbolic geometry: configuration of flags, deformation of representations.

Publications

• The Bohr Theorem for slice regular functions, with C. Della Rocchetta, G. Gentili, Mathematische Nachrichten, vol. 285 (17-18), p. 2093-2105 (2012) doi: 10.1002/mana.201100232 - pdf - arXiv


• A Bloch-Landau theorem for slice regular functions, with C. Della Rocchetta, G. Gentili, in Advances in Hypercomplex Analysis (I. Sabadini, D.C. Struppa, G. Gentili, M. Shapiro, and F. Sommen, editors), Springer INdAM Series, Springer, Milan, 2013 - pdf - arXiv


• Landau-Toeplitz theorems for slice regular functions over quaternions, with G. Gentili, Pacific Journal of Mathematics, vol. 265, no. 2, p. 381-404 (2013) doi: 10.2140/pjm.2013.265.381 - pdf - arXiv


• Invariant metrics for the quaternionic Hardy space, with N. Arcozzi, The Journal of Geometric Analysis, vol. 25, no. 3, p. 2028-2059 (2015) doi: 10.1007/s12220-014-9503-4 - pdf - arXiv


• The orthogonal projection on slice functions on the quaternionic sphere, with N. Arcozzi, in the Proceedings of the 30th International Colloquium on Group Theoretical Methods (F. Brackx, H. De Schepper and J. Van der Jeugt, editors), Journal of Physics: Conference Series, Vol. 597 - pdf - arXiv


• The quaternionic Hardy space and the geometry of the unit ball, Bruno Pini Mathematical Analysis Seminar (2015) doi: 10.6092/issn.2240-2829/5893 - pdf


• Some Hilbert spaces related with the Dirichlet space, with N. Arcozzi, K.M. Perfekt, P. Mozolyako, S. Richter, Concrete Operators, Vol. 3, p. 94-101 (2016) - pdf - arXiv


• Quaternionic Hankel operators and approximation by slice regular functions, Indiana University Mathematics Journal, Vol. 65 (2016) p. 1735-1757 , doi: 10.1512/iumj.2016.65.5896 - pdf - arXiv


• Ideals of regular functions of a quaternionic variable, with G. Gentili, D. C. Struppa, accepted for publication in Mathematical Research Letters - arXiv


• From Hankel operators to Carleson measures in a quaternionic variable, with N. Arcozzi, accepted for publication in the Proceedings of the Edinburgh Mathematical Society - arXiv


• A direct approach to quaternionic regular manifolds, with G. Gentili, A. Gori, Mathematische Nachrichten, Vol. 290, (2017), doi: 10.1002/mana.201500489 - pdf - arXiv


• Quaternionic toric manifolds , with G. Gentili, A. Gori, accepted for publication in the Journal of Symplectic Geometry - arXiv


• The Mittag-Leffler Theorem for regular functions of a quaternionic variable, with G. Gentili, accepted for publication in the New York Journal of Mathematics.


• Quaternionic Hardy spaces, with C. de Fabritiis, G. Gentili, accepted for publication in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze - arXiv

In preparation

• About Carleson measures for the Dirichlet space on the bidisc, with N. Arcozzi, K.M. Perfekt, P. Mozolyako.


• Configuration of flags in orbits of real forms, with E. Falbel, M. Maculan.

Theses

• Elements of function theory in the unit ball of quaternions, PhD Thesis Università di Firenze, 2013 - pdf


• Teoremi di tipo Landau-Toeplitz per funzioni regolari di variabile quaternionica, Master Thesis Università di Firenze, 2009 - pdf


• Excursus sulla dimostrazione della congettura di Poincaré, Bachelor Thesis Università di Firenze, 2007 - pdf