Research & Publications


Research interests

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.

Preprints

  1. Zero sets and Nullstellensatz type theorems for slice regular quaternionic polynomials, with A. Gori, F. Vlacci (arXiv:2212.02301)

  2. Bi-parameter Potential theory and Carleson measures for the Dirichlet space on the bidisc, with N. Arcozzi, P. Mozolyako, K. M. Perfekt (arXiv:1811.04990)


Papers

  1. On compact affine quaternionic curves and surfaces, with G. Gentili, A. Gori, J. Geom. Anal, vol. 31 (2021), 1073 - 1092 (arXiv:1911.06120)

  2. A family of Cauchy-Riemann type operators, with G. Gentili, D. C. Struppa, Riv. Mat. Univ. Parma Vol. 17, (2020), 123 - 138 (link )

  3. Configurations of flags in orbits of real forms, with E. Falbel, M. Maculan, Geom. Dedicata, Vol. 207 (2020) 95-156 (arXiv:1802.10315)

  4. Quaternionic Toric Manifolds, with G. Gentili, A. Gori, J. Symplectic Geom. , 17 (2019), 267-300 (arXiv:1612.03600)

  5. Quaternionic inner and outer functions, with A. Monguzzi, D. Seco, Concr. Oper. , 6 (2019), 44-57 (arXiv:1810.10070)

  6. Slice-Polynomial Functions and Twistor Geometry of Ruled Surfaces in CP^3, with A. Altavilla, Math. Z., 291 (2019), 1059–1092 (arXiv:1712.09946)

  7. Shift invariant subspaces of slice L^2 functions, with A. Monguzzi, Ann. Acad. Sci. Fenn. - M. , 43 (2018), 1045-1061 (arXiv:1802.02344)

  8. Quaternionic Hardy spaces, with C. de Fabritiis, G. Gentili, Ann. Sc. Norm. Super. Pisa Cl. Sci., XVIII (2018), 697-733 (arXiv:1404.1234)

  9. From Hankel operators to Carleson measures in a quaternionic variable, with N. Arcozzi, Proc. Edinb. Math. Soc., 60 (2017), 565-585 (arXiv:1407.8479)

  10. 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)

  11. A direct approach to quaternionic regular manifolds, with G. Gentili, A. Gori, Math. Nachr., 290 (2016) 321-331, (arXiv:1612.03685)

  12. Ideals of regular functions of a quaternionic variable, with G. Gentili, , D.C. Struppa, Math. Res. Lett., 23 (2016), 1645-1663 (arXiv:1611.08827)

  13. Quaternionic Hankel operators and approximation by slice regular functions, Indiana Univ. Math. J., 65 (2016), 1735–1757 (arXiv:1501.02079)

  14. 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)

  15. The quaternionic Hardy space and the geometry of the unit ball, Bruno Pini Mathematical Analysis Seminar, 1 (2015), 103-115

  16. The orthogonal projection on slice functions on the quaternionic sphere, with N. Arcozzi, J. Phys.: Conf. Ser., 597 (2015), 012011 (arXiv:1501.02088)

  17. Invariant metrics for the quaternionic Hardy space, with N. Arcozzi, J. Geom. Anal., 25 (2015), 2028–2059 (arXiv:1312.5906)

  18. Landau-Toeplitz theorems for slice regular functions over quaternions, with G. Gentili, Pacific J. Math., 265 (2013), 381-404 (arXiv:1404.3120)

  19. 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)

  20. The Bohr Theorem for slice regular functions, with C. Della Rocchetta, G. Gentili, Math. Nachr., 285 (2012), 2093-2105 (arXiv:1404.3112)


PhD Thesis

Elements of function theory in the unit ball of quaternions, PhD Thesis, Università degli Studi di Firenze, 2013.