LIST OF PUBLICATIONS


Preprints, work in progress
  1. On the complexity of the truncated moment problem
    D. Henrion, S. Naldi and M. Safey El Din
    — In preparation, 2022

  2. Certifying moment semidefinite representations of convex semialgebraic sets
    D. Henrion and S. Naldi
    — In preparation, 2022

  3. Gröbner bases, syzygies and polynomial matrix multiplication
    S. Naldi and V. Neiger
    — In preparation, 2022


Peer-reviewed publications    (full list on arXiv, see also Hal, orcid.org or scopus)
  1. A divide-and-conquer algorithm for computing Gröbner bases of syzygies in finite dimension
    S. Naldi and V. Neiger
    Proc. 2020 ACM Int. Symp. Symb. Alg. Comput., pp 380-387, 2020

  2. Conic programming: infeasibility certificates and projective geometry
    S. Naldi and R. Sinn
    J. Pure Appl. Algebra 225(7), 2021 - Special Issue of the Arctic Applied Algebra

  3. Spectrahedral representations of plane hyperbolic curves
    M. Kummer, S. Naldi and D. Plaumann
    Pac. J. Math. 303(1):243--263 (2019)

  4. Real root finding for low rank linear matrices
    D. Henrion, S. Naldi and M. Safey El Din
    Appl. Algebr. Eng. Comm. Comp. 31(2), 101-133 (2020) (full-text view-only)

  5. Exact algorithms for semidefinite programs with degenerate feasible set
    D. Henrion, S. Naldi and M. Safey El Din
    J. Symb. Comp. (104) 942--959, 2021
    Proc. 2018 ACM Int. Symp. Symb. Alg. Comput., pp 191-198, 2018

  6. Symbolic computation in hyperbolic programming
    S. Naldi and D. Plaumann
    J. Algebra Appl. 17:10 (2018) (included in the Proceedings of MEGA 2017)

  7. SPECTRA - A Maple library for solving linear matrix inequalities in exact arithmetic
    D. Henrion, S. Naldi and M. Safey El Din
    Optim. Method. Softw. 34(1):62--78 (2019)

  8. Exact algorithms for linear matrix inequalities
    D. Henrion, S. Naldi and M. Safey El Din
    SIAM J. Optimiz. 26(4):2512--2539 (2016)

  9. Solving rank-constrained semidefinite programs in exact arithmetic
    S. Naldi
    J. Symb. Comput. 85C:206--223 (2018)
    Proc. 2016 ACM Int. Symp. Symb. Alg. Comput., pp 357-364, 2016

  10. Real root finding for determinants of linear matrices
    D. Henrion, S. Naldi and M. Safey El Din
    J. Symb. Comput. 74:205--238 (2016)

  11. Real root finding for rank defects in linear Hankel matrices
    D. Henrion, S. Naldi and M. Safey El Din
    Proc. 2015 ACM Int. Symp. Symb. Alg. Comput., pp 221-228, 2015

  12. Nonnegative polynomials and their Carathéodory number
    S. Naldi
    Discrete Comput. Geom. 51(3):559--568 (2014)

Software
  1. SPECTRA — A Maple library for Linear Matrix Inequalities (cf. this paper). The source code of SPECTRA is available here.
  2. HYPER — Implementations of algorithms for Hyperbolic Programming (cf. this paper)
  3. Maple code — from the paper Real root finding for low rank linear matrices.

Other research works
  1. Quantum Random Number Generator based on Violations of the Free CHSH-3 Inequality (with F. Arnault, Don J-B. Anoman) — arXiv pre-print
  2. Patient identification and tumor identification management: quality program in a cancer multicentric clinical data warehouse (with K. Pallier, O. Prot, F. Silva, T. Denis, O. Giry, S. Leobon, E. Deluche, N. Tubiana-Mathieu) — Subm. to Cancer Informatics, 2022
  3. The CHSH inequality for a single qutrit (with D. J. B. Anoman and F. Arnault) — Poster at QCRYPT 2019 (August 2019, Montreal, Canada)
  4. Exact algorithms for determinantal varieties and semidefinite programmingPhD thesis, INSA Université de Toulouse, September 2015 — tel-01212502