RESEARCH
Applied algebra and geometry — Algorithms in real algebraic geometry, systems of polynomial equations and inequalities, syzygies and free resolutions, Gröbner bases
Semialgebraic geometry — Semidefinite Programming, Hyperbolic Polynomials, Conic Programming, positive polynomials and sums of squares
Publications (full list on arXiv, see also Hal, orcid.org or scopus)
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A divide-and-conquer algorithm for computing Gröbner bases of syzygies in finite dimension (with V. Neiger) — ACM ISSAC, Kalamata, GRE (2020), pp. 380-387
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Conic programming: infeasibility certificates and projective geometry
(with R. Sinn) —
J. Pure Appl. Algebra (2020) - AAA Special Issue
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Spectrahedral representations of plane hyperbolic curves (with M. Kummer and D.
Plaumann) — Pac. J. Math. 303(1):243--263 (2019)
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Real root finding for low rank linear matrices (with D. Henrion and M. Safey El Din)
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Appl. Algebr. Eng. Comm. 31(2), 101-133 (2020) (full-text view-only)
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Exact algorithms for semidefinite programs with degenerate feasible set (with D. Henrion and M. Safey El Din)
— J. Symb. Comput. (in press) — ACM ISSAC, NY (2018)
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Symbolic computation in hyperbolic programming (with 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 (with D. Henrion and M. Safey El Din) —
Optim. Method. Softw. 34(1):62--78 (2019)
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Exact algorithms for linear matrix inequalities (with D. Henrion and M. Safey El Din) —
SIAM J. Optimiz. 26(4):2512--2539 (2016)
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Solving rank-constrained semidefinite programs in exact arithmetic —
J. Symb. Comput. 85C:206--223 (2018)
— ACM ISSAC, Waterloo, CAN (2016), pp. 357-364
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Real root finding for determinants of linear matrices (with D. Henrion 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 (with D. Henrion and M. Safey El Din) —
ACM ISSAC, Bath, UK (2015), pp. 221-228
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Nonnegative polynomials and their Carathéodory number —
Discrete Comput. Geom. 51(3):559--568 (2014)
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
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.
Awards/Projects
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PGMO Project «Hyperbolic Programming : Algorithms and Implementations» (Principal Investigator, 2018-2020) — web page
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PEDR (Prime d'Encadrement Doctoral et de Recherche) — 2019-2023
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ANR Project «GEOLMI — Geometry of Linear Matrix Inequalities» (Associate member, 2012-2015) — web page
Collaborators
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Don Jean-Baptiste Anoman — Université de Limoges
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François Arnault — Université de Limoges
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Francesco Ferrante — Université Grenoble Alpes
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Didier Henrion — CNRS LAAS, Czech Technical University in Prague
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Mario Kummer — Technische Universität Berlin
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Vincent Neiger — Université de Limoges
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Daniel Plaumann — Technische Universität Dortmund
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Mohab Safey El Din — Université Pierre et Marie Curie
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Rainer Sinn — Freie Universität Berlin
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