Research

My research lies at the intersection of Commutative Algebra and Algebraic Geometry. I focus on developing algebraic and geometric frameworks to solve problems inspired by applied sciences, with a particular emphasis on tensor decomposition, the geometry of secant varieties, and algebraic statistics.

Find my work: arXiv • ORCID • MathSciNet • Scopus

Hadamard-Hitchcock Decompositions: identifiability and decomposition
with Nick Vannieuwenhoven
Mathematics of Computation, to appear (2026)
arXiv
Postulation for 2-superfat points in the plane
with Stefano Canino, Maria Virginia Catalisano, Sandro Gimigliano, Monica Idà
Annali dell'Università di Ferrara, 71(4):59 (2025)
doi arXiv
Decomposition loci of tensors
with Alessandra Bernardi, Pierpaola Santarsiero
Journal of Symbolic Computation (Special Issue: MEGA 2024), 131:102451 (2025)
DOI arXiv Macaulay2
On schemes evinced by generalized additive decompositions and their regularity
with Alessandra Bernardi, Daniele Taufer
Journal de Mathématiques Pures et Appliquées, 188:446-469 (2024)
DOI arXiv GitHub
Waring decompositions of special ternary forms with different Hilbert functions
with Elena Angelini, Luca Chiantini
Contemporary Mathematics, 805:77-91 (2024)
DOI arXiv
Non-defectivity of Segre-Veronese varieties
with Hirotachi Abo, Maria Chiara Brambilla, Francesco Galuppi
Proceedings of the American Mathematical Society Series B, 11(1):589-602 (2024)
DOI arXiv
Identifiability for mixtures of centered Gaussians and sums of powers of quadratics
with Alex Casarotti, Mateusz Michałek, Alexander Taveira Blomenhofer
Bulletin of London Mathematical Society, 55(5):2407-2424 (2023)
DOI arXiv
Strength and slice rank of forms are generically equal
with Edoardo Ballico, Arthur Bik, Emanuele Ventura
Israel Journal of Mathematics, 254(1):275-291 (2023)
DOI arXiv
Secant non-defectivity via collisions of fat points
with Francesco Galuppi
Advances in Mathematics, 409:108657 (2022)
DOI arXiv
On the strength of general polynomials
with Arthur Bik
Linear and Multilinear Algebra, 70(21):6114-6140 (2022)
DOI arXiv
The set of forms with bounded strength is not closed
with Edoardo Ballico, Arthur Bik, Emanuele Ventura
Comptes Rendus Mathématique, 360:371-380 (2022)
DOI arXiv
Geometric conditions for strict submultiplicativity of rank and border rank
with Edoardo Ballico, Alessandra Bernardi, Fulvio Gesmundo, Emanuele Ventura
Annali di Matematica Pura ed Applicata, 200(1):187-210 (2021)
DOI arXiv
On minimal decompositions of low rank symmetric tensors
with Bernard Mourrain
Linear Algebra and its Applications, 607:347-377 (2020)
DOI arXiv Macaulay2
Unexpected curves arising from special line arrangements
with Michela Di Marca, Gregorz Małara
Journal of Algebraic Combinatorics, 51(2):171-194 (2020)
DOI arXiv
Tangential varieties of Segre-Veronese surfaces are never defective
with Maria Virginia Catalisano
Revista Matematica Complutense, 33(1):95-324 (2020)
DOI arXiv
On the Hilbert function of general fat points in \(\mathbb{P}^1\times\mathbb{P}^1\)
with Enrico Carlini, Maria Virginia Catalisano
Michigan Mathematical Journal, 69(3):601-632 (2020)
DOI arXiv
The monic rank
with Arthur Bik, Jan Draisma, Emanuele Ventura
Mathematics of Computation, 89(325):2481-2505 (2020)
DOI arXiv
On generic and maximal k-ranks of binary forms
with Samuel Lundqvist, Boris Shapiro, Bruce Reznick
Journal of Pure and Applied Algebra, 223(5):2062-2079 (2019)
DOI arXiv
Partially symmetric variants of Comon's problem via simultaneous rank
with Fulvio Gesmundo, Emanuele Ventura
SIAM Journal on Matrix Analysis and Applications, 40(4):1453-1477 (2019)
DOI arXiv
On the quantum periods of del Pezzo surfaces with \(\frac{1}{3}(1,1)\) singularities
with Andrea Petracci
Advances in Geometry, 18(3):303-336 (2018)
DOI arXiv
Waring-like decompositions of polynomials, 1
with Maria Virginia Catalisano, Luca Chiantini, Anthony Vito Geramita
Linear Algebra and Its Applications, 533:311-325 (2017)
DOI arXiv
Waring loci and the Strassen conjecture
with Enrico Carlini, Maria Virginia Catalisano
Advances in Mathematics, 314:630-662 (2017)
DOI arXiv
On the real rank of monomials
with Enrico Carlini, Mario Kummer, Emanuele Ventura
Mathematische Zeitschrift, 286(1-2):571-577 (2017)
DOI arXiv
Minkowski sums and hadamard products of algebraic varieties
with Netaniel Friedenberg, Robert L. Williams
Fields Institute Communications vol. 80, Combinatorial Algebraic Geometry (eds. G. G. Smith, B. Sturmfels), 133-157 (2017)
DOI arXiv
Mirror symmetry and the classification of orbifold del pezzo surfaces
with M. Akthar, T. Coates, A. Corti, L. Heuberger, A. Kasprzyk, A. Petracci, T. Prince, K. Tveiten
Proceedings of the American Mathematical Society, 144(2):513-527 (2016)
DOI arXiv
On a class of power ideals
with Joergen Backelin
Journal of Pure and Applied Algebra, 219(8):3158-3180 (2015)
DOI arXiv
Monomials as Sums of k-th powers of forms
with Enrico Carlini
Communications in Algebra, 43(2):650-658 (2015)
DOI arXiv
Ranks of tensors: geometry and applications
with Emanuele Ventura
Bollettino dell'Unione Matematica Italiana, 18(3):751-778 (2025)
DOI
The Hitchhiker guide to: Secant varieties and tensor decomposition
with Alessandra Bernardi, Enrico Carlini, Maria Virginia Catalisano, Alessandro Gimigliano
Mathematics, 6(12):314 (2018), special issue: Decomposability of Tensors (ed. L. Chiantini)
DOI arXiv
Algebraic Stories from One and from the Other Pockets
with Ralf Fröberg, Samuel Lundqvist, Boris Shapiro
Arnold Mathematical Journal, 4(2):137-160 (2018)
DOI arXiv
Hadamard ranks of algebraic varieties
with Dario Antolini, Guido Montúfar
arXiv:2510.05231 (2025)
arXiv Zenodo
Polynomials of small slice rank and strength
with Cosimo Flavi, Fulvio Gesmundo, Emanuele Ventura
arXiv:2509.12322 (2025)
arXiv
Algebraic surfaces as Hadamard products of curves
with Dario Antolini, Edoardo Ballico
arXiv:2502.18813 (2025)
arXiv Zenodo
Algebraic and geometric properties of minimal tensor rank decompositions
BM60: Bernard Mourrain's 60th Birthday, Leipzig, Germany (August 2024)
Slides (PDF)
Hadamard-Hitchcock Decompositions
TAGA 2024 (Tensors: Algebra, Geometry and Applications), Fort Collins (June 2024)
SIAM Conference on Applied Algebraic Geometry, Eindhoven (July 2023)
Slides (PDF)
Identifiability of centered Gaussian Mixtures and sums of powers of quadratics
Joint Mathematical Meeting 2023, Boston (January 2023)
Slides (PDF)
On the strength of general polynomials
SIAM Conference on Applied Algebraic Geometry, Texas A&M U. (August 2021)
TensorTalk, QMATH, U. Copenhagen (May 2020)
Slides (PDF)
Secant non-defectivity of Segre-Veronese varieties via collapsing points
AMS-EMS-SMF International Meeting, Grenoble (July 2022)
MEGA, U. Tromsø (June 2021)
Slides (PDF)
Variants of Comon's problem via simultaneous rank
Congresso UMI, U. Pavia (September 2019)
SIAM Conference on Applied Algebraic Geometry, U. Bern (July 2019)
Slides (PDF)
Waring loci and decompositions of low rank symmetric tensors
Workshop for Young Researchers in Mathematics, U. Bucharest (June 2019)
Discrete Math. Seminar, U. Bern (November 2018)
Seminari di Algebra e Geometria, Poli. Milano (December 2018)
Slides (PDF)
A new question on planar polynomial interpolation and line arrangements
IPPI Workshop, Poli. Torino (March 2018)
Seminari di Algebra e Geometria, U. Genova (February 2018)
Slides (PDF)
Hilbert function of general fat points in \(\mathbb{P}^1\times\mathbb{P}^1\)
Seminari de Geometria Algebraica, U. Barcelona (February 2018)
Workshop on Syzygies, U. Trento (September 2017)
Slides (PDF)