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 (with V. Neiger) — ACM ISSAC, Kalamata, GRE (2020), pp. 380-387
2. Conic programming: infeasibility certificates and projective geometry (with R. Sinn) — J. Pure Appl. Algebra (2020) - AAA Special Issue
3. Spectrahedral representations of plane hyperbolic curves (with M. Kummer and D. Plaumann) — Pac. J. Math. 303(1):243--263 (2019)
4. Real root finding for low rank linear matrices (with D. Henrion and M. Safey El Din) — Appl. Algebr. Eng. Comm. 31(2), 101-133 (2020) (full-text view-only)
5. 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)
   
6. Symbolic computation in hyperbolic programming (with 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 (with D. Henrion and M. Safey El Din) — Optim. Method. Softw. 34(1):62--78 (2019)
8. Exact algorithms for linear matrix inequalities (with D. Henrion and M. Safey El Din) — SIAM J. Optimiz. 26(4):2512--2539 (2016)
9. Solving rank-constrained semidefinite programs in exact arithmetic — J. Symb. Comput. 85C:206--223 (2018) — ACM ISSAC, Waterloo, CAN (2016), pp. 357-364
10. Real root finding for determinants of linear matrices (with D. Henrion and M. Safey El Din) — J. Symb. Comput. 74:205--238 (2016)
11. 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
12. Nonnegative polynomials and their Carathéodory number — Discrete Comput. Geom. 51(3):559--568 (2014)

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

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.

Awards/Projects

1. PGMO Project  «Hyperbolic Programming : Algorithms and Implementations»  (Principal Investigator, 2018-2020) — web page
   
2. PEDR (Prime d'Encadrement Doctoral et de Recherche) — 2019-2023
   
3. ANR Project  «GEOLMI — Geometry of Linear Matrix Inequalities»  (Associate member, 2012-2015) — web page
   

Collaborators

1. Don Jean-Baptiste Anoman — Université de Limoges
2. François Arnault — Université de Limoges
3. Francesco Ferrante — Université Grenoble Alpes
4. Didier Henrion — CNRS LAAS, Czech Technical University in Prague
5. Mario Kummer — Technische Universität Berlin
6. Vincent Neiger — Université de Limoges
7. Daniel Plaumann — Technische Universität Dortmund
8. Mohab Safey El Din — Université Pierre et Marie Curie
9. Rainer Sinn — Freie Universität Berlin