My research interests are in the area of complex and hypercomplex analysis and geometry. In particular I am interested in:
slice regular functions over the quaternions and applications: geometric theory, quaternionic Hardy spaces, Hankel operators, Carleson measures, invariant subspaces, slice regularity and orthogonal complex structures, Nullstellensatz type results;
quaternionic geometry: quaternionic regular manifolds, quaternionic toric manifolds, quaternionic affine 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.
Quaternionic Carleson measures, with N. Chalmoukis (arXiv:2512.06831)
On the irreducibility of slice algebraic sets, with A. Gori, F. Vlacci (arXiv:2507.21674)
Zero sets and Nullstellensatz type theorems for slice regular quaternionic polynomials, with A. Gori, F. Vlacci, Journal of Algebra, (2026), 687, pp. 269–291
Resultants of slice regular polynomials in two quaternionic variables, with A. Gori, F. Vlacci, Computer Aided Geometric Design 2024, 114, 102381
Bi-parameter Potential theory and Carleson measures for the Dirichlet space on the bidisc, with N. Arcozzi, P. Mozolyako, K. M. Perfekt, Discrete Analysis, 2023, pp. 1–57
On compact affine quaternionic curves and surfaces, with G. Gentili, A. Gori, J. Geom. Anal, vol. 31 (2021), 1073 - 1092 (arXiv:1911.06120)
A family of Cauchy-Riemann type operators, with G. Gentili, D. C. Struppa, Riv. Mat. Univ. Parma Vol. 17, (2020), 123 - 138 (link )
Configurations of flags in orbits of real forms, with E. Falbel, M. Maculan, Geom. Dedicata, Vol. 207 (2020) 95-156 (arXiv:1802.10315)
Quaternionic Toric Manifolds, with G. Gentili, A. Gori, J. Symplectic Geom. , 17 (2019), 267-300 (arXiv:1612.03600)
Quaternionic inner and outer functions, with A. Monguzzi, D. Seco, Concr. Oper. , 6 (2019), 44-57 (arXiv:1810.10070)
Slice-Polynomial Functions and Twistor Geometry of Ruled Surfaces in CP^3, with A. Altavilla, Math. Z., 291 (2019), 1059–1092 (arXiv:1712.09946)
Shift invariant subspaces of slice L^2 functions, with A. Monguzzi, Ann. Acad. Sci. Fenn. - M. , 43 (2018), 1045-1061 (arXiv:1802.02344)
Quaternionic Hardy spaces, with C. de Fabritiis, G. Gentili, Ann. Sc. Norm. Super. Pisa Cl. Sci., XVIII (2018), 697-733 (arXiv:1404.1234)
From Hankel operators to Carleson measures in a quaternionic variable, with N. Arcozzi, Proc. Edinb. Math. Soc., 60 (2017), 565-585 (arXiv:1407.8479)
The Mittag-Leffler Theorem for regular functions of a quaternionic variable, with G. Gentili, New York J. Math, 23 (2017), 583-592 (arXiv:1711.05064)
A direct approach to quaternionic regular manifolds, with G. Gentili, A. Gori, Math. Nachr., 290 (2016) 321-331, (arXiv:1612.03685)
Ideals of regular functions of a quaternionic variable, with G. Gentili, , D.C. Struppa, Math. Res. Lett., 23 (2016), 1645-1663 (arXiv:1611.08827)
Quaternionic Hankel operators and approximation by slice regular functions, Indiana Univ. Math. J., 65 (2016), 1735–1757 (arXiv:1501.02079)
Some Hilbert Spaces related with the Dirichlet space, with N. Arcozzi, P. Mozolyako, K.M. Perfekt, S. Richter, Concr. Oper., 3 (2016), 94-101 (arXiv:1512.07532)
The quaternionic Hardy space and the geometry of the unit ball, Bruno Pini Mathematical Analysis Seminar, 1 (2015), 103-115
The orthogonal projection on slice functions on the quaternionic sphere, with N. Arcozzi, J. Phys.: Conf. Ser., 597 (2015), 012011 (arXiv:1501.02088)
Invariant metrics for the quaternionic Hardy space, with N. Arcozzi, J. Geom. Anal., 25 (2015), 2028–2059 (arXiv:1312.5906)
Landau-Toeplitz theorems for slice regular functions over quaternions, with G. Gentili, Pacific J. Math., 265 (2013), 381-404 (arXiv:1404.3120)
A Bloch-Landau Theorem for slice regular functions, with C. Della Rocchetta, G. Gentili, Advances in Hypercomplex Analysis (I. Sabadini, D.C. Struppa, G. Gentili, M. Shapiro, and F. Sommen, editors), 55-74, Berlin/Heidelberg: Springer (2013) (arXiv:1404.3117)
The Bohr Theorem for slice regular functions, with C. Della Rocchetta, G. Gentili, Math. Nachr., 285 (2012), 2093-2105 (arXiv:1404.3112)
Elements of function theory in the unit ball of quaternions, PhD Thesis, Università degli Studi di Firenze, 2013.