Papers and Preprints

Preprints:

On the codimension of permanental varieties (with A. Boralevi, E. Carlini and M. Michałek), preprint, 2024.

Border apolarity and varieties of sums of powers (with T.  Mańdziuk), preprint, 2023.

Tensors with maximal symmetries (with A. Conner, F. Gesmundo, and J.M. Landsberg), preprint, 2021.

Research publications: 

Quasihomomorphisms from the integers into Hamming metrics (with J. Draisma, R. Eggermont, T. Seynnaeve, and N. Tairi), Algebr. Comb., to appear, 2024. 

Implicitisation and parameterisation in polynomial functors (with A. Blatter and J. Draisma), Found. Comput. Math., to appear, 2023. 

A note on very ample Terracini loci (with E. Ballico), Rend. Circ. Mat. Palermo (2), to appear, 2023.

Degrees of Kalman varieties of tensors (with Z. Shahidi and L. Sodomaco), J. Symb. Comput. (special vol. MEGA 2021),114:74-98, 2023.

The set of forms with bounded strength is not closed (with E. Ballico, A. Bik, A. Oneto), C. R. Math. Acad. Sci. Paris, 360:371-380, 2022.

Strength and slice rank of forms are generically equal (with E. Ballico, A. Bik, A. Oneto), Israel J. Math., 254: 275-291, 2023.

Kronecker powers of tensors and Strassen's laser method (with A. Conner, F. Gesmundo, and J.M. Landsberg), Comput. Complexity, 31(1), 2022.

Asymptotics of degrees and ED degrees of Segre products (with G. Ottaviani and L. Sodomaco), Adv. Appl. Math., 130, 102242, 2021.

The strength for line bundles (with E. Ballico), Math. Scand., 127(2021), 405-440.

Vanishing Hessian, wild forms and border VSP (with H. Huang and M. Michałek), Math. Ann., 378:1505-1532, 2020.

Injective linear series of algebraic curves on quadrics (with E. Ballico), Ann. Univ. Ferrara Sez. VII Sci. Mat., 66(2):231-254, 2020.

Strict inclusions of high rank loci (with E. Ballico and A. Bernardi), J. Symb. Comput. (special vol. MEGA 2019), (109):238-249, 2022.

Entry loci and ranks (with E. Ballico), Manuscripta Math., 165(3): 559-581, 2021.

Geometric conditions for strict submultiplicativity of rank and border rank (with E. Ballico, A. Bernardi, F. Gesmundo, and A. Oneto), Ann. Mat. Pura Appl., 200(1):187-210, 2021.

Towards a geometric approach to Strassen's asymptotic rank conjecture (with A. Conner, F. Gesmundo, J.M. Landsberg and Y. Wang), Collect. Math., 72(1):63-86, 2021.

Singular curves of low degree and multifiltrations from osculating spaces (with J. Buczyński and N. Ilten), Int. Math. Res. Not. IMRN, Vol. 2020, No. 21, 8139-8182, 2020.

Labels of real projective varieties (with E. Ballico), Boll. dell'Unione Mat. Ital. (BUMI),  13(2):257-273, 2020.

The monic rank (with A. Bik, J. Draisma and A. Oneto), Math. Comp., 89(325):2481-2505, 2020.

Minimal degree equations for curves and surfaces (variations on a theme of Halphen) (with E. Ballico), Beiträge Algebra Geom., 61(2):297-315, 2020.

Partially symmetric variants of Comon's problem via simultaneous rank (with F. Gesmundo and A. Oneto), SIAM J. Matrix Anal. Appl.(SIMAX), 40(4), 1453-1477, 2019.

A note on the simultaneous Waring rank of monomials (with E. Carlini), Illinois J. Math, 61(3-4):517-530, 2017.

Real rank boundaries and loci of forms, Linear Multilinear Algebra, 67(7):1404-1419, 2019.

Phylogenetic complexity of the Kimura 3-parameter model (with M. Michałek), Adv. Math., 343, 640-680, 2019.

Finite phylogenetic complexity and combinatorics of tables (with M. Michałek), Algebra Number Theory, 11(1):235-252, 2017.

On the real rank of monomials (with E. Carlini, M. Kummer and A. Oneto), Math. Z., 286(2):571-577, 2016.

Real rank geometry of ternary forms (with M. Michałek, H. Moon and B. Sturmfels), Ann. Mat. Pura Appl., 196(3):1025-1054, 2016.

The poset of proper divisibility (with D. Bolognini, A. Macchia and V. Welker), SIAM J. Discrete Math., 31(3):2093-2109, 2017.

Real and complex Waring rank of reducible cubic forms (with E. Carlini and C. Guo), J. Pure Appl. Algebra, 220(11):3692-3701, 2016.

Refereed conference proceedings:

On the Koiran-Skomra's question about Hessians (with E. Ballico),  AMS Contemporary Math., Proceedings for Special Session "Deformation of Artinian Algebras  and Jordan Types" (AMS-EMS-SMF Meeting, Grenoble),  AMS, 2024. 

Kronecker powers of tensors and Strassen's laser method (with A. Conner, F. Gesmundo, and J.M. Landsberg), LIPIcs, Vol. 151, ITCS 2020, 10:1-10:28.

Lecture notes: 

An introduction to eigenvectors of tensors, lecture notes for a 5 hours mini-course at the introductory school of of the AGATES semester.

Thesis:

Geometry of real tensors and phylogenetics, PhD Thesis, Aalto University, 2017.