Journal papers

  • A Quadratically Convergent Algorithm for Structured Low-Rank Approximation.
    With Eric Schost.
    Foundations of Computational Mathematics. 1-36, 2015.
    Arxiv. Maple code.
  • Exact Solutions in Structured Low-Rank Approximation.
    With Giorgio Ottaviani and Bernd Sturmfels.
    SIAM Journal on Matrix Analysis and Applications. 35(4):1521-1542, 2014.
    [pdf] [bib].
  • On the Complexity of Computing Critical Points with Gröbner Bases.
    SIAM Journal on Optimization. 24(3):1382-1401, 2014.
    [pdf] [bib] abstract.
  • On the Complexity of the Generalized MinRank Problem.
    With Jean-Charles Faugère, Mohab Safey El Din.
    Journal of Symbolic Computation. 55:30-58, 2013.
    [pdf] [bib] abstract.
  • On the Complexity of Solving Quadratic Boolean Systems.
    With Magali Bardet, Jean-Charles Faugère, Bruno Salvy.
    Journal of Complexity, 29(1):53-75, 2013.
    [pdf] [bib] abstract.
  • Gröbner Bases of Bihomogeneous Ideals generated by Polynomials of Bidegree (1,1): Algorithms and Complexity.
    With Jean-Charles Faugère, Mohab Safey El Din.
    Journal of Symbolic Computation, 46(4):406-437, 2011.
    [pdf] [bib] Magma Code abstract.

Articles in conference proceedings

  • Critical points computations on smooth varieties: degree and complexity bounds.
    With Mohab Safey El Din. Proceedings of the International Symposium on Symbolic and Algebraic Computation 2016 (ISSAC 2016).
    Held in Waterloo, Canada.

    Arxiv.
  • Computing small certificates of inconsistency of quadratic fewnomial systems.
    With Jean-Charles Faugère and Jules Svartz. Proceedings of the International Symposium on Symbolic and Algebraic Computation 2016 (ISSAC 2016).
    Held in Waterloo, Canada.

    Arxiv.
  • Sparse Gröbner Bases: the Unmixed Case.
    With Jean-Charles Faugère, Jules Svartz.
    Proceedings of the International Symposium on Symbolic and Algebraic Computation 2014 (ISSAC 2014).
    Held in Kobe, Japan.

    Arxiv.
  • Critical Points and Gröbner Bases: the Unmixed Case.
    With Jean-Charles Faugère, Mohab Safey El Din.
    Proceedings of the International Symposium on Symbolic and Algebraic Computation 2012 (ISSAC 2012).
    Held in Grenoble, France.

    [pdf] [bib]
  • Computing Loci of Rank Defects of Linear Matrices using Gröbner Bases and Applications to Cryptology.
    With Jean-Charles Faugère, Mohab Safey El Din.
    Proceedings of the International Symposium on Symbolic and Algebraic Computation 2010 (ISSAC 2010).
    Held in Munich, Germany.

    Distinguished Student Author Award.
    [pdf] [bib] slides abstract.
  • Algebraic Cryptanalysis of the PKC'09 Algebraic Surface Cryptosystem.
    With Jean-Charles Faugère.
    Proceedings of the 13th International Conference on Practice and Theory in Public Key Cryptography (PKC 2010).
    Held in Paris, France.

    [pdf] [bib] slides Magma Code abstract.

Preprints and notes

  • Sparse polynomial systems with many positive solutions from bipartite simplicial complexes.
    With Frédéric Bihan. Preprint. In revision. Arxiv.
  • Computing the rho constant.
    With Jérémie Detrey and Paul Zimmermann. Short note on the computation of the density of integer numbers such that the number of distinct prime factors has the same parity as the number prime factors counted with multiplicity. Note (pdf).

Ph.D. thesis

  • Solving multi-homogeneous and determinantal systems.
    Algorithms - Complexity - Applications.

    Supervisors: Jean-Charles Faugère, Mohab Safey El Din.
    PolSys project-team (INRIA/UPMC/LIP6).
    Université Pierre et Marie Curie, 2012.
    [pdf][bib]
    [Erratum]

Posters

  • Newton-like Iteration for Determinantal Systems and Structured Low-Rank Approximation.
    Eric Schost, Pierre-Jean Spaenlehauer.
    International Symposium on Symbolic and Algebraic Computation 2013 (ISSAC 2013).
    Held in Boston, USA.

    abstract[pdf].

Talks in workshops and conferences

  • Critical points computations on smooth varieties: degree and complexity bounds. ISSAC 2016. Waterloo, Ontario, Canada. July 20-22, 2016.
  • Computing small certificates of inconsistency of quadratic fewnomial systems. ISSAC 2016. Waterloo, Ontario, Canada. July 20-22, 2016.
  • Sparse polynomial systems with many positive solutions from bipartite simplicial complexes.
    • Workshop on Algebra, Geometry and Proofs in Symbolic Computation. Fields Institute, Toronto, Canada. December 7-16, 2015.
  • A quadratically convergent algorithm for Structured Low-Rank Approximation.
    • ICIAM 2015, Workshop on hybrid methodologies for symbolic-numeric computations, Beijing, China, August 10-13, 2015.
    • RAIM 2013. Institut Henri Poincaré, Paris, France. November 18-20, 2013.
    • Numerical methods and computations. CIRM, Luminy, France. October 28-31, 2013.
  • Exact solutions in structured low-rank approximation.
    • SIAM Conference on Applied Algebraic Geometry. Daejeon, Korea, August 3-7, 2015. Minisymposium on ML Degree and Critical Points.
    • SLRA workshop. Grenoble, France. June, 1, 2015.
  • Sparse Gröbner bases: the unmixed case.
    • SIAM Conference on Applied Algebraic Geometry. Daejeon, Korea, August 3-7, 2015. Minisymposium on Algorithms and Complexity in Polynomial Systems.
    • Conference on Effective Moduli Spaces and Applications to Cryptology. Rennes, France. June, 12, 2014.
  • Gröbner bases and bilinear systems.
    DLP 2014. Ascona, Switzerland. May, 06, 2014.
  • Solving Determinantal and Quadratic Boolean Systems. Applications to Algebraic Cryptanalysis.
    Journées C2 2014. Grenoble, France. March, 26, 2014.
    slides[pdf]
  • Critical Points and Gröbner Bases: the Mixed Case.
    • Workshop on Gröbner Bases, Resultants and Linear Algebra. RISC, Hagenberg, Austria. September 3-6, 2013.
    • SIAM Conference on Applied Algebraic Geometry. Fort Collins, CO, USA. August 1-4, 2013. Mini-Symposium on Algorithms in Real Algebraic Geometry.
  • Critical Points and Gröbner Bases: the Unmixed Case.
    ISSAC 2012. Grenoble, France. July 22-25, 2012.
  • On the Complexity of Solving Boolean Quadratic Systems.
    SIAM Conference on Applied Algebraic Geometry. Raleigh, NC, USA. October 6-9, 2011. Mini-Symposium on Algebraic Complexity.
  • Gröbner bases of Structured Systems and their Applications in Cryptology.
    MAYA Workshop 2011. Bochum, Germany. July 28-29, 2011.
    slides[pdf]
  • Computing Loci of Rank Defects of Linear Matrices using Gröbner Bases and Applications to Cryptology.
    ISSAC 2010. Munich, Germany. July 25-28, 2010.
    slides[pdf]
  • Algebraic Cryptanalysis of the PKC'09 Algebraic Surface Cryptosystem.
    PKC 2010. Paris, France. May 26-28, 2010.
    slides[pdf]
  • Algebraic-Differential Cryptanalysis of DES.
    Weworc 2009. Graz, Austria. July 7-9, 2009.
    summary[pdf] slides[pdf]

Talks in seminars

  • Computing small certificates of inconsistency of quadratic fewnomial systems.
    • Séminaire de Géométrie. Chambéry, France, Apr. 12, 2017.
  • Critical points computations on smooth varieties: degree and complexity bounds.
    • Séminaire de Géométrie. Chambéry, France, Apr. 7, 2016.
  • Sparse polynomial systems with many positive solutions from bipartite simplicial complexes.
    • Séminaire AriC, LIP, ENS Lyon. Lyon, France, June 9, 2016.
    • Symbolic Computation Group, University of Waterloo. Waterloo, Canada, May 24, 2016.
    • Journées Nationales du Calcul Formel. Cluny, France, Nov. 2-6, 2015.
  • On the complexity of computing critical points with Gröbner bases.
    • University of Neuchatel, Switzerland. 12/08, 2014.
  • Sparse Gröbner bases: the unmixed case
    • LIRMM, Montpellier, France. 03/04, 2015.
    • Séminaire de géométrie, LAMA. Chambéry, France. 12/12, 2014.
    • Western University, CS department. London, Ontario, Canada. 06/04, 2014.
  • A Newton-like iteration and algebraic methods for Structured Low-Rank Approximation.
    • Séminaire de Calcul Formel. Rennes, France. 11/28, 2014.
    • Séminaire Caramel. Nancy, France. 03/13, 2014.
    • Séminaire Calcul Formel. Limoges, France. 03/06, 2014.
    • Séminaire SpecFun. Palaiseau, France. 03/03, 2014.
    • Séminaire ARIC. Lyon, France. 02/27, 2014.
  • Critical Points, Gröbner Bases and Structured Low Rank Approximation.
    • Technische Universiteit. Eindhoven, Netherlands. 12/11, 2013.
    • Dipartimento di Matematica e Informatica U. Dini. Florence, Italy. 10/23, 2013.
  • A quadratically convergent algorithm for Structured Low-Rank Approximation.
    • Séminaire PolSys. LIP6/UPMC/INRIA, Paris, France. 09/27, 2013.
  • Gröbner bases of Structured Systems and their Applications in Cryptology and in Geometry.
    • Séminaire Crypto. PrisM, UVSQ, Versailles, France. 01/09, 2013.
    • Séminaire CARAMEL. LORIA, Nancy, France. 01/17, 2013.
    • Séminaire Calcul Formel et Complexité. IRMAR, Rennes, France. 01/18, 2013.
    • SCPQ Webinar. 03/08, 2012.
  • On the Complexity of Solving Boolean Quadratic Systems.
    • Séminaire ARIC. ENS Lyon, France. 10/11, 2012.
    • Journées Nationales du Calcul Formel. CIRM, Luminy, France. 11/17, 2011.
  • Algebraic Cryptanalysis of the PKC'09 Algebraic Surface Cryptosystem.
    • Séminaire Cryptographie et Sécurité. PRISM/UVSQ, Versailles 04/28, 2011.
  • Computing Critical Points with Gröbner Bases: Complexity and Applications to Polynomial Minimization.
    • Max Planck Institute for Mathematics. Bonn, Germany 07/29, 2013.
    • Séminaire Combinatoire et Algorithmes. LITIS, Rouen 02/23, 2012.
    • Séminaire Salsa. LIP6/UPMC/INRIA 12/09, 2011.
    • Séminaire Salsa. LIP6/UPMC/INRIA 02/11, 2011.
    • Séminaire Algorithms. INRIA Paris/Rocquencourt 01/31, 2011.
  • Bilinear Systems and Determinantal Varieties. Application to MinRank.
    • Journées Codage et Cryptographie. Oléron 04/05, 2011.
    • Séminaire Cryptologie. Rennes 10/08, 2010.
    • Journées nationales du calcul formel. CIRM, Luminy 05/03, 2010. Summary[pdf].
  • Gröbner Bases of Bihomogeneous Ideals Generated by Polynomials of Bidegree (1,1): Algorithms, Complexity and Applications.
    • Séminaire Salsa: structured systems. LIP6/UPMC/INRIA 07/09, 2010.
    • Séminaire Algorithms. INRIA Paris/Rocquencourt 04/26, 2010. slides[pdf].
  • Algebraic-Differential Cryptanalysis of DES.
    • Journées nationales "Codage et Cryptographie". Fréjus 10/05, 2009. slides[pdf].
    • Séminaire de Cryptologie. Caen 10/29, 2009. slides[pdf].
    • Séminaire SALSA. Paris 07/03, 2008.