Research Activities of Thomas Cluzeau

Field of research: Computer algebra and applications:

• Algorithmic study of systems of linear functional (differential, (q)-difference, partial differential) equations, closed form solutions, factorization, decomposition

• Algebraic analysis approach to linear systems theory, effective homological algebra, applications to control theory
• Multidimensional (nD) systems: equivalence, stability, stabilization

• Polynomial vector fields, first integrals, Darboux polynomials

• Differential algebra, differential elimination and applications to control theory

Implementations

• Spencer (soon!) : A Maple package for studying formal integrability of linear systems of PDEs (with C. Chenavier and A. Quadrat)
  
  
• Bavula (new!) : A Maple package for linear ordinary polynomial integro-differential systems (with C. Pinto and A. Quadrat)
  
  
• OreAlgebraicAnalysis: A Mathematica package for the algorithmic study of linear functional systems (with A. Quadrat and Maris Tõnso)

• RationalFirstIntegrals : A Maple package for computing rational first integrals and Darboux polynomials of planar polynomial 
  vector fields (with A. Bostan, G. Chèze, and J.-A. Weil)

• IntegrableConnections : A Maple package for computing rational and hyperexponential solutions of linear systems of PDEs written as integrable connections (with M. A Barkatou, C. El Bacha, and J.-A. Weil)
• OreMorphisms: A Maple package for factoring, reducing and decomposing linear functional systems (with A. Quadrat).
• The Maple package InterfaceConditionsReduction developed in the project SADDLES  and dedicated to the symbolic development of new domain decomposition
  algorithms based on Smith normal forms, Gröbner basis computation and constructive algebraic analysis (with V.Dolean, F. Nataf, and A. Quadrat).
  See Symbolic methods for developing new domain decomposition algorithms and the example files ReductionProblem and CompletionProblem

• SystemTheory: A homalg package (GAP4) dedicated to mathematical system theory (with M. Barakat, M. Lange-Hegermann, and A. Quadrat).  
• FactorModp: Maple procedures for decomposing and factoring differential systems in characteristic p.

Cours JNCF 2020

· Les transparents de mon cours aux Journées Nationales de Calcul Formel 2020 : transparents

PhD students

• Carole El Bacha (2008-2011, with M. A. Barkatou)
• Ali El Hajj (2017-2021, with M. A. Barkatou)
• Camille Pinto (Starting in October 2022, with A. Quadrat)
• Adya Musson-Leymarie (Starting in October 2023, with C. Chenavier)

Other students I’ve worked with

· Quentin Helman (Doctorant Université de Limoges – publications communes, projet MIRES)

· Maya Chartouni (co-encadrement stage de Master 2, 2021, avec A. Quadrat)

· Ronan David (Doctorant University of Poitiers – publications communes – projets ANR MSDOS, MIRES)

· Alexandre Rigaud (Doctorant University of Poitiers – publications communes – projets MIRES)

· Achref Jalouli (Doctorant University of Limoges – publication commune)

· Abdelkarim Chakar (co-encadrement 2 années de doctorat University of Limoges, avec A. Quadrat – publication commune)