Highlights
- Bernstein-Gelfand-Gelfand meets geometric complexity theory: resolving the 2 x 2 permanents of a 2 x n matrix,
with A. Huang, H. Schenck, J. Weyman
Trans. Am. Math. Soc., vol. 378(5), pp. 3573-3596 (2025) journal arXiv - Fixed-parameter debordering of Waring rank,
with P. Dutta, C. Ikenmeyer, G. Jindal, V. Lysikov,
STACS 2024, Leibniz International Proceedings in Informatics (LIPIcs), 289, pp. 30:1-30:15 (2024) conference arXiv - A Gap in the Subrank of Tensors,
with M. Christandl, J. Zuiddam,
SIAM J. Applied Alg. and Geom., vol. 7 (4), pp. 742-767 (2023) journal arXiv
Presented at QIP 2024: link - Dimension of Tensor Network Varieties,
with A. Bernardi, C. De Lazzari,
Communications in Contemporary Mathematics, vol. 25(10), pp.2250059 (2023) journal arXiv code
Presented at MEGA 2021: slides - Rank and border rank of Kronecker powers of tensors and Strassen's laser method
with A. Conner, J. M. Landsberg, E. Ventura
computational complexity, 31, 1, (2022) journal arXiv code
ITCS 2020, Leibniz International Proceedings in Informatics (LIPIcs), 151, 10:1--10:28 (2020) conference code
All publications
- Marvelous slices of orthogonal matrices,
with T. Brysiewicz
to appear Experimental Mathematics, (2026), preprint - Algebraic metacomplexity and representation theory,
with M. van den Berg, P. Dutta, C. Ikenmeyer, V. Lysikov
40th Computational Complexity Conference, CCC 2025, vol. 339, pp. 26:1--26:35, (2025) journal arXiv - Geometric complexity theory for product-plus-power,
with P. Dutta, C. Ikenmeyer, G. Jindal, V. Lysikov,
J. Symbolic Computation, vol. 132, pp. 102458, (2025) journal arXiv - The next gap in the subrank of 3-tensors,
with J. Zuiddam
Linear Algebra and its Applications, vol. 722. pp. 1--11 (2025) journal arXiv - Linear preservers of secant varieties and other varieties of tensors,
with B. Lovitz, Y. Han
J. Symbolic Computation, vol. 131, pp. 102449, (2025) journal arXiv - Bernstein-Gelfand-Gelfand meets geometric complexity theory: resolving the 2 x 2 permanents of a 2 x n matrix,
with A. Huang, H. Schenck, J. Weyman
Trans. Am. Math. Soc., vol. 378(5), pp. 3573-3596 (2025) journal arXiv - Collineation varieties of tensors,
with H. Keneshlou
Collectanea Mathematica, online first (2025) journal arXiv code - Hilbert Functions of Chopped Ideals,
with L. Kayser, S. Telen,
Journal of Algebra, 666, pp. 415-445 (2025) journal arXiv code
The Mathrepo page of this article was awarded the Fairest Mathrepo Page 2023 Award. - Quantum max-flow in the bridge graph,
with V. Lysikov, V. Steffan,
Transformation Groups, vol. 30, pp. 1751-1784 (2025) journal arXiv - Quatroids and Rational Plane Cubics,
with T. Brysiewicz, A. Steiner
Beiträge zur Algebra und Geometrie, 65(4), pp. 923-972 (2024) journal arXiv - Fixed-parameter debordering of Waring rank,
with P. Dutta, C. Ikenmeyer, G. Jindal, V. Lysikov,
STACS 2024, Leibniz International Proceedings in Informatics (LIPIcs), 289, pp. 30:1-30:15 (2024) conference arXiv - Homogeneous Algebraic Complexity Theory and Algebraic Formulas,
with P. Dutta, C. Ikenmeyer, G. Jindal, V. Lysikov,
ITCS 2024, Leibniz International Proceedings in Informatics (LIPIcs), 287, pp. 43:1-43:23 (2024) conference arXiv - Partial Degeneration of Tensors,
with M. Christandl, V. Lysikov, V. Steffan,
SIAM Journal on Matrix Analysis and Applications (SIMAX), 45(1), pp. 771-800 (2024) journal arXiv - Decompositions and Terracini loci of cubic forms of low rank,
with L. Chiantini,
Deformation of Artinian Algebras and Jordan Types, Contemporary Mathematics, vol. 805, pp. 139-156 (2024) volume arXiv - A Gap in the Subrank of Tensors,
with M. Christandl, J. Zuiddam,
SIAM J. Applied Alg. and Geom., vol. 7 (4), pp. 742-767 (2023) journal arXiv
Presented at QIP 2024: link - Geometry of Tensors: Open problems and research directions,
A report on the AGATES Kickoff Workshop (2023), Agates arXiv - Algebraic Compressed Sensing,
with P. Breiding, M. Michałek, N. Vannieuwenhoven,
Applied and Computational Harmonic Analysis, vol. 65, pp.374-406 (2023) journal arXiv - Dimension of Tensor Network Varieties,
with A. Bernardi, C. De Lazzari,
Communications in Contemporary Mathematics, vol. 25(10), pp.2250059 (2023) journal arXiv code
Presented at MEGA 2021: slides - Degree-restricted strength decompositions and algebraic branching programs,
with P. Ghosal, C. Ikenmeyer, V. Lysikov,
FSTTCS 2022, Leibniz International Proceedings in Informatics (LIPIcs), 250, 20:1-20:15 (2022) conference arXiv - The Geometry of Discotopes,
with C. Meroni,
Le Matematiche, 77 (1), 143--171, (2022) journal arXiv - Rank and border rank of Kronecker powers of tensors and Strassen's laser method
with A. Conner, J. M. Landsberg, E. Ventura
computational complexity, 31, 1, (2022) journal arXiv code
ITCS 2020, Leibniz International Proceedings in Informatics (LIPIcs), 151, 10:1--10:28 (2020) conference code - Optimization at the boundary of the tensor network variety,
with M. Christandl, D. Stilck-França, A. H. Werner,
Physical Review B 103 (19), 195139 (2021) journal arXiv - The Degree of Stiefel Manifolds,
with T. Brysiewicz,
Enumerative Combinatorics and Applications, vol. 1(3), n.S2R20, (2021) journal arXiv - Border rank non-additivity for higher order tensors,
with M. Christandl, M. Michałek, J. Zuiddam,
SIAM Journal on Matrix Analysis and Applications (SIMAX), 42(2), 503–527 (2021) journal arXiv - Geometric conditions for strict submultiplicativity of rank and border rank
with E. Ballico, A. Bernardi, A. Oneto, E. Ventura
Annali di Matematica Pura ed Applicata - vol. 200, 187--210 (2021) journal arXiv - Towards a Geometric Approach to Strassen's Asymptotic Rank Conjecture
with A. Conner, J. M. Landsberg, E. Ventura, Y. Wang
Collectanea Mathematica - vol. 72, 63--86 (2021) journal arXiv - SARS-CoV-2 transmission routes from genetic data: a Danish case study
with A. Bluhm, M. Christandl, F. R. Klausen, L. Mančinska, V. Steffan, D. Stilck França, A. H. Werner
PLoS One, 15(10), e0241405 (2020) journal bioRxiv - Partially symmetric versions of Comon's problem via simultaneous rank
with A. Oneto, E. Ventura
SIAM Journal on Matrix Analysis and Applications (SIMAX) 40(4), 1453--1477 (2019) journal arXiv - Explicit polynomial sequences with maximal spaces of partial derivatives and a question of K. Mulmuley
with J. M. Landsberg
Theory of Computing 15(3), 1--24, (2019) journal arXiv - Border rank is not multiplicative under the tensor product
with M. Christandl, A. K. Jensen
SIAM J. Appl. Alg. Geom (SIAGA), Vol. 3 (2), 231--255 (2019) journal arXiv - On the partially symmetric rank of tensor product of W-states and other symmetric tensors
with E. Ballico, A. Bernardi, M. Christandl
Rendiconti Lincei di Matematica e Applicazioni, Vol. 30, issue 1, pp. 93--124 (2019) journal arXiv - A note on the cactus rank for Segre-Veronese varieties
with E. Ballico, A. Bernardi
Journal of Algebra, Vol. 526, pp. 6--11 (2019) journal arXiv - Matrix Product States and the Quantum max-flow/min-cut conjectures
with J. M. Landsberg, M. Walter
Journal of Mathematical Physics, Vol. 59 (10), 102205 (2018) journal arXiv - Geometric Complexity Theory and matrix powering
with C. Ikenmeyer, G. Panova
Differential Geometry and its Applications, Vol. 55, 106--127 (2017) journal arXiv - Geometric Aspects of Iterated Matrix Multiplication
Journal of Algebra, Vol. 461, pp.42--64, (2016) journal arXiv - Complexity of linear circuits and geometry
with J. Hauenstein, C. Ikenmeyer, J. M. Landsberg
Foundations of Computational Mathematics (FOCM), Vol. 16 (3), 599--635, (2016) journal arXiv - An asymptotic bound for secant varieties of Segre varieties
Annali dell'Università di Ferrara, Vol. 59 (2), 285-302, (2013) journal arXiv
Preprints
- Schubert compactifications of matrix pencils,
with V. Galgano, H. Keneshlou
preprint
- Computing the continuous symmetries of a parametrized variety,
with B. Biaggi, J. Draisma, A. Maraj, M. Mišinová
preprint
Accepted for a presentation at MEGA 2026. - Border subrank of higher order tensors and algebras,
with C.-Y. Chang, J. Zuiddam
preprint - Triangular tensor networks, pencils of matrices and beyond,
with A. Bernardi
preprint - Waring decompositions of special binomials,
with L. Chiantini, S. Marziali
preprint - Polynomials of small slice rank and strength,
with C. Flavi, A. Oneto, E. Ventura
preprint
Accepted for a presentation at MEGA 2026. - Identifiability through special linear measurements,
with A. Grosdos, A. Uschmajew
preprint - Characteristic polynomials and eigenvalues of tensors,
with F. Galuppi, E. Teixeira Turatti, L. Venturello
preprint code - Tensors with maximal symmetries,
with A. Conner, J. M. Landsberg, E. Ventura,
preprint
PhD Thesis
- Geometry and Representation Theory in the Study of Matrix Rigidity, Thesis, 2017.
Master's Thesis
- Tensori e Varietà Secanti, (in Italian) -- Thesis, 2012.
Notes
These notes are not intended for publication (at least, not in their current form).