Preprints

1. On semidefinite-representable sets over valued fields (C. Cornou, S. Naldi and T. Vaccon). Technical report, January 2026 — arXiv/....
2. Solving generic parametric linear matrix inequalities (S. Naldi, M. Safey El Din, A. Taylor and W. Wang). Technical report, January 2026 — arXiv/....
3. On the configurations of four spheres supporting the vertices of a tetrahedron (M. Longinetti and S. Naldi) Technical Report, May 2024 — arXiv/2405.16167.
   
4. Algebraic certificates for the truncated moment problem (D. Henrion, S. Naldi and M. Safey El Din) Technical Report, January 2023 — arXiv/2302.06927.
   

Publications    (full list on arXiv, see also Hal, orcid.org or scopus)

1. R-hulloid of the vertices of a tetrahedron (M. Longinetti, S. Naldi and A. Venturi) to appear in Adv. Appl. Maths. (2025) -- preprint at arXiv/2406.00658.
   
2. Solving generic parametric linear matrix inequalities (S. Naldi, M. Safey El Din, A. Taylor and W. Wang). ACM Int. Symp. Symb. Alg. Comput., pp 267--276 (2025).
   
3. Certifying solutions of degenerate semidefinite programs (V. Kolmogorov, S. Naldi and J. Zapata) SIAM J. Opt. 35(3):1630-1654 (2025). [full-text view-only]
   [an extended abstract appeared in the ACM Comm. Comput. Alg. (2025)]
   
4. Taylor polynomials of rational functions (A. Conca, S. Naldi, G. Ottaviani and B. Sturmfels) Acta Math. Vietn. 49:19--37 (2024) [full-text view-only]
   
5. Patient identification and tumor identification management: quality program in a cancer multicentric clinical data warehouse (K. Pallier et al) Cancer Inform. 2023 May 19;22:11769351231172609
   
6. A divide-and-conquer algorithm for computing Gröbner bases of syzygies in finite dimension (S. Naldi and V. Neiger) ACM Int. Symp. Symb. Alg. Comput., pp 380-387, 2020
   
7. 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
   
8. Spectrahedral representations of plane hyperbolic curves (M. Kummer, S. Naldi and D. Plaumann) Pac. J. Math. 303(1):243--263 (2019)
   
9. 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]
   
10. 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
    [preliminary version published in the proceedings of ACM Int. Symp. Symb. Alg. Comput., pp 191-198, 2018]
    
11. Symbolic computation in hyperbolic programming (S. Naldi and D. Plaumann) J. Algebra Appl. 17:10 (2018) (included in the Proceedings of MEGA 2017)
    
12. SPECTRA - A Maple library for solving linear matrix inequalities in exact arithmetic (D. Henrion, S. Naldi and M. Safey El Din) Opt. Meth. Softw. 34(1):62--78 (2019)
    
13. Exact algorithms for linear matrix inequalities (D. Henrion, S. Naldi and M. Safey El Din) SIAM J. Opt. 26(4):2512--2539 (2016)
    
14. Solving rank-constrained semidefinite programs in exact arithmetic (S. Naldi) J. Symb. Comput. 85C:206--223 (2018)
    [preliminary version published in the proceedings of ACM Int. Symp. Symb. Alg. Comput., pp 357-364, 2016]
    
15. Real root finding for determinants of linear matrices (D. Henrion, S. Naldi and M. Safey El Din) J. Symb. Comput. 74:205--238 (2016)
    
16. Real root finding for rank defects in linear Hankel matrices (D. Henrion, S. Naldi and M. Safey El Din) ACM Int. Symp. Symb. Alg. Comput., pp 221-228, 2015
    
17. Nonnegative polynomials and their Carathéodory number (S. Naldi) Discrete Comput. Geom. 51(3):559--568 (2014)

Projects

1. Gröbner bases, syzygies and polynomial matrix multiplication (in collaboration with V. Neiger).
   
2. Sharp bounds for the sphere crossing radius of some families of tetrahedra (in collaboration with M. Longinetti)
   
3. Certifying moment semidefinite representations of convex semialgebraic sets (in collaboration with D. Henrion).
   

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.
4. Macaulay2/Maple code — from the paper On the configurations of four spheres supporting the vertices of a tetrahedron.

Other research works

1. The CHSH inequality for a single qutrit (with D. J. B. Anoman and F. Arnault) — Poster at QCRYPT 2019 (August 2019, Montreal, Canada)
2. Exact algorithms for determinantal varieties and semidefinite programming — PhD thesis, INSA Université de Toulouse, September 2015 — tel-01212502
3. Quantum random number generator based on violations of the free CHSH-3 inequality (F. Arnault, S. Naldi and Don J-B. Anoman) July 2020, arXiv/2003.00124