Fulvio Gesmundo

Institut de Mathématiques de Toulouse - Université Paul Sabatier

My articles are also on Google Scholar and arXiv. You can check out my Orcid.

If you need access to one of my articles, feel free to contact me.


  1. Fixed-parameter debordering of Waring rank, with P. Dutta, C. Ikenmeyer, G. Jindal, V. Lysikov,
    to appear STACS 2024, arXiv
  2. 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
  3. Partial Degeneration of Tensors, with M. Christandl, V. Lysikov, V. Steffan,
    to appear SIAM J. Matrix An. (SIMAX), arXiv
  4. A Gap in the Subrank of Tensors, with M. Christandl, J. Zuiddam,
    SIAM J. Applied Alg. and Geom., vol. 7 (4), pp. 742-767, journal arXiv
    Presentation at QIP 2024: link
  5. Decompositions and Terracini loci of cubic forms of low rank, with L. Chiantini,
    to appear in Deformation of Artinian Algebras and Jordan Types, CONM, 2023 arXiv
  6. Geometry of Tensors: Open problems and research directions,
    A report on the AGATES Kickoff Workshop (2023), Agates arXiv
  7. Algebraic Compressed Sensing, with P. Breiding, M. Michałek, N. Vannieuwenhoven,
    Applied and Computational Harmonic Analysis, vol. 65, pp.374-406 (2023) journal arXiv
  8. 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
  9. 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
  10. The Geometry of Discotopes, with C. Meroni,
    Le Matematiche, 77 (1), 143--171, (2022) journal arXiv
  11. 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
  12. 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
  13. The Degree of Stiefel Manifolds, with T. Brysiewicz,
    Enumerative Combinatorics and Applications, vol. 1(3), n.S2R20, (2021) journal arXiv
  14. Border rank non-additivity for higher order tensors, with M. Christandl, M. Michałek, J. Zuiddam,
    SIAM Journal on Matrix Analysis and Applications, 42(2), 503–527 (2021) journal arXiv
  15. 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
  16. 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
  17. 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
  18. 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
  19. 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
  20. 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
  21. 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
  22. 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
  23. 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
  24. Geometric Complexity Theory and matrix powering with C. Ikenmeyer, G. Panova
    Differential Geometry and its Applications, Vol. 55, 106--127 (2017) journal arXiv
  25. Geometric Aspects of Iterated Matrix Multiplication
    Journal of Algebra, Vol. 461, pp.42--64, (2016) journal arXiv
  26. Complexity of linear circuits and geometry J. Hauenstein, C. Ikenmeyer, J. M. Landsberg
    Foundations of Computational Mathematics (FOCM), Vol. 16 (3), 599--635, (2016) journal arXiv
  27. An asymptotic bound for secant varieties of Segre varieties
    Annali dell'Università di Ferrara, Vol. 59 (2), 285-302, (2013) journal arXiv


  1. 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
  2. Collineation varieties of tensors, with H. Keneshlou
  3. Quatroids and Rational Plane Cubics, with T. Brysiewicz, A. Steiner
  4. Characteristic polynomials and eigenvalues of tensors, with F. Galuppi, E. Teixeira Turatti, L. Venturello
    preprint code
  5. The next gap in the subrank of 3-tensors, with J. Zuiddam
  6. Hilbert Functions of Chopped Ideals, with L. Kayser, S. Telen,
    preprint code
    The Mathrepo page of this article was awarded the “Who is the FAIRest” Prize.
  7. Quantum max-flow in the bridge graph, with V. Lysikov, V. Steffan,
  8. De-bordering and Geometric Complexity Theory for Waring rank and related models, with P. Dutta, C. Ikenmeyer, G. Jindal, V. Lysikov,
  9. Tensors with maximal symmetries, with A. Conner, J. M. Landsberg, E. Ventura,

PhD Thesis:

Master's Thesis:


These notes are not intended for publication (at least, not in their current form).

  1. An example of non-semialgebraic intersection body, link, 2022
  2. Introduction to Enumerative Geometry, link, 2021
    Notes for the course taught at MPI-MiS.
  3. A short note on Induced Representations, link, 2014