LIST OF PUBLICATIONS
Preprints
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R-hulloid of the vertices of a tetrahedron
(M. Longinetti, S. Naldi and A. Venturi)
June 2024, arXiv/2406.00658, submitted.
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On the configurations of four spheres supporting the vertices of
a tetrahedron
(M. Longinetti and S. Naldi)
May 2024, arXiv/2405.16167, submitted.
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Algebraic certificates for the truncated moment problem
(D. Henrion, S. Naldi and M. Safey El Din)
January 2023, arXiv/2302.06927.
Publications (full list on arXiv, see also Hal, orcid.org or scopus)
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Solving generic parametric linear matrix inequalities
(S. Naldi, M. Safey El Din, A. Taylor and W. Wang).
ACM Int. Symp. Symb. Alg. Comput., to appear (2025) - preprint available on arXiv/2503.01487.
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Certifying solutions of degenerate semidefinite programs
(V. Kolmogorov, S. Naldi and J. Zapata)
SIAM J. Opt., to appear (2025) - preprint available on arXiv/2405.13625.
[extended abstract to appear in the ACM Comm. Comput. Alg. (2025)]
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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]
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Patient identification and tumor identification management: quality program in a cancer multicentric clinical data warehouse
(K. Pallier, O. Prot, S. Naldi, F. Silva, T. Denis, O. Giry, S. Leobon, E. Deluche, N. Tubiana-Mathieu)
Cancer Inform. 2023 May 19;22:11769351231172609
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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
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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
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Spectrahedral representations of plane hyperbolic curves
(M. Kummer, S. Naldi and D. Plaumann)
Pac. J. Math. 303(1):243--263 (2019)
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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]
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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]
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Symbolic computation in hyperbolic programming
(S. Naldi and D. Plaumann)
J. Algebra Appl. 17:10 (2018) (included in the Proceedings of MEGA 2017)
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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)
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Exact algorithms for linear matrix inequalities
(D. Henrion, S. Naldi and M. Safey El Din)
SIAM J. Opt. 26(4):2512--2539 (2016)
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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]
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Real root finding for determinants of linear matrices
(D. Henrion, S. Naldi and M. Safey El Din)
J. Symb. Comput. 74:205--238 (2016)
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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
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Nonnegative polynomials and their Carathéodory number
(S. Naldi)
Discrete Comput. Geom. 51(3):559--568 (2014)
Projects
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On semidefinite-representable sets over valued fields
(in collaboration with C. Cornou and T. Vaccon).
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Gröbner bases, syzygies and polynomial matrix multiplication
(in collaboration with V. Neiger).
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Sharp bounds for the sphere crossing radius of some families of tetrahedra
(in collaboration with M. Longinetti)
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Certifying moment semidefinite representations of convex semialgebraic sets
(in collaboration with D. Henrion).
Software
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SPECTRA — A Maple library for Linear Matrix Inequalities (cf. this paper). The source code of SPECTRA is available here.
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HYPER — Implementations of algorithms for Hyperbolic Programming (cf. this paper)
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Maple code — from the paper Real root finding for low rank linear matrices.
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Macaulay2/Maple code — from the paper On the configurations of four spheres supporting the vertices of a tetrahedron.
Other research works
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The CHSH inequality for a single qutrit (with D. J. B. Anoman and F. Arnault) — Poster at QCRYPT 2019 (August 2019, Montreal, Canada)
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Exact algorithms for determinantal varieties and semidefinite programming — PhD thesis, INSA Université de Toulouse, September 2015 — tel-01212502
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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
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