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)
  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 arithmeticJ. 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 numberDiscrete 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 programmingPhD 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