Research Interests

• Real and Complex Differential Geometry - Riemannian manifolds, Hermitian and Kähler manifolds.

• Lie Theory - Lie groups and Lie algebras, (local) Lie transformation groups on manifolds, (locally) homogeneous spaces.

• Geometric Analysis - convergence of Riemannian manifolds, geometric flows, elliptic PDE on Riemannian manifolds.

Papers

• (with D. Angella, S. Calamai, C. Spotti) A moment map for twisted-Hamiltonian vector fields on locally conformally Kähler manifolds, to appear in Transformation Groups.

        DOI:  10.1007/s00031-023-09815-2

        Online version: arXiv:2207.06863

• (with D. Angella) A survey on locally homogeneous almost-Hermitian spaces, Riv. Mat. Univ. Parma 13 (2021), 373-418.

         Online version: arXiv:2111.14577

• (with A. Goffi) Sobolev regularity for nonlinear Poisson equations with Neumann boundary conditions on Riemannian manifolds, Forum Math 35 (2023), 431-456.

• (with S. Sbiti) Collapsed ancient solutions of the Ricci flow on compact homogeneous spaces, Proc. Lond. Math. Soc. 125 (2022), 1130-1151.

• (with D. Angella) On cohomogeneity one Hermitian non-Kähler metrics, Proc. Roy. Soc. Edinburgh Sect. A. 153 (2023), 545-587.

• (with D. Angella) On the linearization stability of the Chern-scalar curvature, Math. Z. 301 (2022), 1675-1693.

• (with A. Goffi) A note on the strong maximum principle for fully nonlinear equations on Riemannian manifolds, J. Geom. Anal. 31 (2021), 8641-8665.

         DOI: 10.1007/s12220-021-00607-2

         Preprint version: arXiv:2007.15448

• A compactness theorem for locally homogeneous spaces, Ann. Sc. Norm. Super. Pisa Cl. Sci. 23 (2022), 339-360.

         DOI: 10.2422/2036-2145.201912_001

         Preprint version: arXiv:1911.05062

• Convergence of locally homogeneous spaces, Geom. Dedicata 211 (2021), 105-127.

         DOI: 10.1007/s10711-020-00542-6

         Preprint version: arXiv:1911.12627

• (with M. Pujia) Hermitian Curvature Flow on complex locally homogeneous surfaces, Ann. Mat. Pura Appl. 200 (2021), 815-844.

         DOI: 10.1007/s10231-020-01015-z

         Preprint version: arXiv:1906.11676

• A local version of the Myers-Steenrod Theorem, Bull. Lond. Math. Soc. 52 (2020), 871-884.

         DOI: 10.1112/blms.12367

         Preprint version: arXiv:1906.02988

• Diverging sequences of unit volume invariant metrics with bounded curvature, Ann. Glob. Anal. Geom. 56 (2019), 519-553.

         DOI: 10.1007/s10455-019-09677-6

         Preprint version: arXiv:1812.08074

• Chern-Dirac bundles on non-Kähler Hermitian manifolds, Rocky Mountain J. Math. 48 (2018), 1255-1290.

         DOI: 10.1216/RMJ-2018-48-4-1255

         Preprint version: arXiv:1704.06211

Preprints & current projects

• (with A. M. Krishnan, S. Sbiti) Toral symmetries of collapsed ancient solutions to the homogeneous Ricci flow, submitted

Thesis

• Geometric aspects of locally homogeneous Riemannian spaces, PhD thesis, Università di Firenze.