MOULAY A. BARKATOU
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  Systems of Ordinary Differential Equations (Global and Local Solutions, Positive or Zero Characteristic, First or Higher Order)

  • M. Barkatou : On the Newton polygon of  a Moser-irreducible differential system to appear in the post-proceedings of of the conference FASDiff17. Volume "Formal and Analytic Solutions of diff. Equations" in Springer Proceedings in Mathematics & Statistics.
  • M. Barkatou, J. Saade, J.A. Weil:  A new approach for formal reduction of singular linear differential systems using eigenrings, to appear in the proceedings of   ISSAC'18.
  • M. Barkatou et G. Renat  :  Smallness of the formal exponents of an irregular differential system with an application to solvability by quadratures,  Computer Algebra International Conference Moscow 2017  UDC 517.927.7   pages : 11-16
  • Barkatou, Moulay; Cluzeau, Thomas; Ovchinnikov, Alexey; Regensburger, Georg; Rosenkranz, Markus; Special issue on computational aspects of differential/difference algebra and integral operators. Adv. in Appl. Math. 72 (2016)
  • S. Abramov, M. Barkatou, and D. Khmelnov.  On Full Rank Differential Systems with Power Series Coefficients,  Journal of Symbolic Computation (2015) : Volume 68, Part 1,  pp 120-137    http://dx.doi.org/10.1016/j.jsc.2014.08.010.

  • Sergei Abramov and Moulay Barkatou Computable infinite power series in role of coefficients of linear differential systems.  LNCS 8660, CASC 2014: 1-12

  • S. Abramov and M. A. Barkatou. On Solution Spaces of Products of Linear Differential or Difference Operators. To appear in  ACMCCA 2014.
  • Moulay A. Barkatou, Thomas Cluzeau, Georg Regensburger, Markus Rosenkranz (Eds.): Algebraic and Algorithmic Aspects of Differential and Integral Operators - 5th International Meeting, AADIOS 2012, Held at the Applications of Computer Algebra Conference, ACA 2012, Sofia, Bulgaria, June 25-28, 2012, Selected and Invited Papers. Lecture Notes in Computer Science 8372, Springer 2014, ISBN 978-3-642-54478-1 .
 

  Systems of Difference Equations
  • M. Barkatou, M. Jaroschek: Desingularization of First Order Linear Difference Systems with Rational  Function Coefficients, to appear in the proceedings of   ISSAC'18.
  • Barkatou, M. A., Cluzeau, T., El Bacha, C., On the computation of simple forms and regular solutions of linear difference systems.
    Advances in Computer Algebra, Springer  Proceedings in Mathematics & Statistices (2018), volume  226, pages 19-49,   C. Schneider; E. Zima  (Eds.)

  Systems of Linear Partial Differential Equations / Integrable Connections
  • Moulay A. Barkatou, Maximilian Jaroschek, Suzy S. Maddah: Formal solutions of completely integrable Pfaffian systems with normal crossings. J. Symb. Comput. 81: 41-68 (2017)
  • M. Barkatou, Suzy S, Maddah, and H. Abbas: On the Reduction of Singularly-Perturbed Linear Differential Systems. Proceedings of  the International Symposium on Symbolic and Algebraic Computations (ISSAC), July 21-25, Kobe, Japan. A preliminary version is available at: arXiv:1401.5438
    .
  • M. Barkatou, Suzy S, Maddah, and H. Abbas: Formal Solutions of a Class of Pfaffian Systems in Two Variables. To appear appear in the Proceedings of  the International Symposium on Symbolic and Algebraic Computations (ISSAC), July 21-25, Kobe, Japan.A preliminary version is available at: arXiv:1401.5439 .

  • Moulay A. Barkatou, Thomas Cluzeau, Carole El Bacha, Jacques-Arthur Weil: Computing Closed-Form Solutions of Integrable Connections. Proceedings of the International Symposium on Symbolic and Algebraic Computations (ISSAC), july 22-25, Grenoble, France, 2012. ISSAC 2012: 43-50

  • Nicolas LeRoux, Moulay A. Barkatou: Rank Reduction of a Class of Pfaffian Systems in two variables, Proceedings of the 2006 International Symposium on Symbolic and Algebraic Computation, ACM, New York, Pages 204—211. ISSAC 2006

  • Moulay Barkatou, Thomas Cluzeau, Jacques-Arthur Weil: Factoring Partial Differential Systems in Positive Characteristic. D. Wang (Ed.), Differential Equations with Symbolic Computation (DESC Book),pages 213-238, Birkhaüser (2005).

  Systems of Singularly-Perturbed Linear Differential Systems
  • M. Barkatou, Suzy S. Maddah, and H. Abbas: On the Reduction of Singularly-Perturbed Linear Differential Systems.  Proceedings of  the International Symposium on Symbolic and Algebraic Computations (ISSAC), July 21-25, Kobe, Japan. A preliminary version is available at: arXiv:1401.5438
 
  Locally Nilpotent Derivations (LND) and their Applications
 
  Matrix Polynomials
  • S. Abramov, M. Barkatou : On Strongly Non-Singular Polynomial Matrices,
    Advances in Computer Algebra, Springer  Proceedings in Mathematics & Statistices (2018), volume  226, pages 1-17,   C. Schneider; E. Zima  (Eds.)
  • Moulay A. Barkatou, Paola Boito, E. Sehura Uglade,  ``A contour integral approach to the computation of invariant pairs"
    Theor. Comput. Sci. 681: 3-26 (2017)
  • Moulay A. Barkatou, Paola Boito, and E. Segura Ugalde: Some ideas for the computation of matrix solvents. SNC 2014: 19-20.
  
  Other invited talks and presentations:
  • « On the Asymptotic Solutions of Systems of Differential Equations at Irregular Singularities ». Workshop on Nonlinear Analysis and Applications 2012, Mehdia, Tunisia, December 16-19, 2012.
  •  « Solving Linear Ordinary Differential Systems in Closed Form ». LSMS Third Annual Meeting. (LSMS-2012), The American University of Beirut, Beirut, April 27-28, 2012.
  • « On the Exponential Parts of Singular Linear Differential Equations ». The second conference ``Symbolic Computation and its Applications" May 17-20, 2012, RWTH Aachen University, Germany.
  • « On the Exponential Parts of Linear Differential Equations with Meromorphic Coefficients and Their Computation ». Functional Equations in LIMoges 2012, Analytic and algebraic approaches to integrability, March 5-7, 2012.
  • « Symbolic Methods for Solving Systems of Linear Ordinary Differential Equations », June 13-17, 2011, Lehrstuhl B für Mathematik, RWTH Aachen University Germany,
  •  « Removing Apparent Singularities of Systems of Linear Differential Equations with Rational Function Coefficients ». The Second Workshop Differential Equations by Algebraic Methods (DEAM2), February 9–11, 2011, JKU Linz
  •  « On the Problem of Removing Apparent Singularities of Linear Differential Equations with Polynomial Coefficients », Applications of Computer Algebra (ACA) 2010, University of Vlora, Vlora, Albania, 24-27 June, 2010
  • « Local Reduced Forms of Systems of Linear Functional Equations and Applications », Applications of Computer Algebra (ACA) 2009, Montreal, Canada, juin 2009,
  •  « On Subanalytic Solutions of Linear Difference Equations with Polynomial Coefficients », Seminario Iberoamericano de Matemàticas, Singularidades en Tordesillas, Instituto Interunivesitario de Iberoam\'etica, 21 abril de 2009.
  •  « On Entire Solutions of Linear Difference Equations with Polynomial Coefficients » , Premier colloque Franco-Tunisien de Mathématiques, 16-20 mars 2009, Djerba, Tunisie.
  •  « Hypergeometric Solutions of Systems of Linear Difference Equations and Applications », Seminar ALGO, INRIA Rocquencourt, Paris, Octobre 2008.
  •  « Hypergeometric Solutions of Systems of Linear Difference Equations and Applications » Symbolic Analysis Workshop \@ FoCM, Hong Kong. June 24-26, 2008.
  •  « Factorization and Hypergeometric Solutions of Linear Difference Equations» Seminar at the Key Laboratory of Mathematics Mechanization. Academy of Mathematics and Systems Science. Beijing- China. June 19 , 2008.
  •  « Sur les séries d'Alambertiennes solutions d'équations différentielles linéaires à coefficients polynomiaux »
  • Premier colloque franco-maghrebin du calcul formel, du 23 au 26 mai 2008- Sfax - Iles de Kerkennah.
  • « Reduced Forms of Systems of Linear Functional Equations and Applications » 12-th Workshop On Computer Algebra, The Joint Institute for Nuclear Research, May 14-16, 2008, Dubna, Russia
  • « Direct Symbolic Methods for Solving Systems of Linear Differential Equations », Waterloo University, July 2007
  • « On the Formal Solutions of Linear Systems of Differential Equations near a Singular Point », 11th Workshop On Computer Algebra, The Joint Institute for Nuclear Research, May 24-25, 2007, Dubna, Russia
  •  « On D'Alembertian Series Solutions of Linear Ordinary Differential Equations with Polynomial Coefficients », 11-th Workshop On Computer Algebra, The Joint Institute for Nuclear Research, May 24-25, 2007, Dubna, Russia
  •  « Direct algebraic methods for solving systems of linear differential équations », Workshop Algebraic Theory of Differential Equations, Heriot-Watt University, Edinburgh, 31 July to 11 August 2006,
  •  « Exponential Parts of Singular Differential Equations », Waterloo Workshop on Computer Algebra, Waterloo Workshop on Computer Algebra, Waterloo, Ontario, CANADA, 10-12 Avril 2006,
  • « Rational Solutions of Linear Differential Systems », Journées ``Hamilton", Limoges July, 3-6 2006
  • « On the exponential parts of the formal solutions of a linear differential system », Fondations of Computational Mathematics, Workshop on Computational Dynamics, Santander, July 7-9 2005
  •  « Removing Apparent Singularities of Linear Difference Equations with Polynomial Coefficients », International Conference on Constructive and Computational Mathematics, Marrakech, December 14-17 2005
  •  « Desingularization of Difference Operators », Seminar CAFE, INRIA Sophia- Antipolis, October2004
  • « Continuation Of Holomorphic Solutions Of Linear Differential Equations With Polynomial Coefficients. », International Conference Kolmogorov And Contemporary Mathematics, Moscow, June 16-21, 2003.
  •  « Rank Reduction of Linear Differential Systems with an Irregular Singularity », Computer Algebra Group Seminar, University of Marralesh, September 2003.
  • « Sur la réduction de systèmes d'équations pseudo-linéaires » Séminaire du Laboratoire de Mathématiques Calcul Asymptotique, Université de La Rochelle, Avril 2001.
  •  « Sur la factorisation de systèmes d'équations pseudo-linéaires », Séminaire d'Analyse numérique, Université de Rabat Maroc, Décembre 2000.
  •  « Sur les problèmes d'équivalence et de factorisation de systèmes aux différences linéaires. », Journées Equations différentielles et calcul formel, Lille du 16 au 18 mars 2000
  •  « Solving matrix difference equations with rational coefficients » SCG Seminar, University of Waterloo, Canada, July 1999.
  •  « Equivalence de deux systèmes différentiels linéaires et applications", Colloque « Panorama de calcul formel » Marrakech, Maroc Mai 10-14 1999.

  • « Direct Methods for Computing Rational Solutions of Linear Differential Systems », Mathematics Colloquium, San Diego State University, September 1998
  •  « Rational Solutions of linear differential and difference systems », Seminar "Symbolic Computations" MSRI, Berkeley, USA, September 1998.
  •  « An Algorithm for Computing the Formal Invariants of Linear Difference System », (with Guoting CHEN) ASCM'98 August 6-8, 1998, Lanzhou, China, Proceedings of ASCM'98 Zhibin Li (Ed.), Lanzhou University Press.
  •  « Gevrey character of formal solutions of a differential-difference equation with polynomial coefficients », Workshop « Asymptotic Theory and Multisummability of Power Series in Several Variables », June 24-27, 1998, Fabri-Institute, Blaubeuren, Germany.
  •  « Recent developments in ISOLDE » , Cathode-2 Castillo de La Mota Workshop, May 11-16, 1998, Medina del Campo, Spain.
  •  « An algorithm for the Computation of the Exponential Part of Formal Solutions of Difference Systems » (with G. Chen), The Sixth Rhine Workshop on Computer Algebra, March 31.- April 3, 1998, Sankt Augustin, Germany.
  •  « ISOLDE: a package for Integrating Systems of Linear Differential Equations », Cathode 2 Workshop, Han sur less, Belgique , 1-5 september 1997
  •  « A fast algorithm to compute the rational solutions of systems of linear differential équations » Workshop « Symbolic-Numeric Analysis of Differential Equations » (SNADE'97) Prague, June 16- 18 1997.
  •  « Formes super-irr éductibles et leurs applications à la recherche de solutions rationnelles d'équations différentielles »,
  •  dans le cadre du séminaire Equations fonctionnelles » université de Strasbourg I, Février 1997
  •  « Un algorithme rapide pour le calcul des solutions rationnelles d'un système différentiel linéaire », Séminaire ALGO, INRIA Rocquencourt, Paris, January 1997.
  •  « On Rational Solutions Of Linear Differential Systems », Journées sur la théorie de Galois algébrique et différentielle , Rennes, november 1996.
  •  « On the formal solutions of difference-differential équations », The 2nd Marrakesh International Conference on Differential Equations", Marrakech june 1995.
  •  « Formal solutions of an irregular linear differential system », The 3rd CATHODE workshop, London, Queen Mary and Westfield College, London March 1994.
  • « On formal solution of linear difference équations », The 2nd Cathode Conference, Dagstuhl, RFA, september 1993.
  • « Solutions formelles d'équations aux différences polynomiales » aux « Journées sur les équations aux différences », Strasbourg, février 1993.
  • « An Algorithm for Computing Rational Forms Systems of Linear Differential Equations », Computer Algebra and Differential Equations (CADE), Luminy, june 1992.
  •  « Sur les syst\`emes diff\'erentiels lin\'eaires singuliers », Journées « Calcul formel, intégration, équations différentielles », Limoges 1991
  •  « Caractérisation des systèmes aux différences à singularité régulière », Workshop « Calcul formel en théorie des systèmes", Gif sur Yvette, mars 1989.
  • «Optimisation de DESIR pour les équations différentielles du second ordre », Computer Algebra and Differential Equations (CADE) Grenoble 1988, Proceedings CADE 1988, ACM Press (1989).