Laboratoire de Physique Théorique

de la Matière Condensée

ABDELAZIZ Youssef

 



Mon sujet de thèse : Séries à coefficients entiers solutions d'équations différentielles linéaires et non linéaires en physique

Mon Directeur de thèse Jean Marie Maillard

 

ALGEBRAIC STATISTICAL MECHANICS

Diagonals of rational functions, Ising model, susceptibility of the Ising model, Yang-Baxter equations, Integrability, lattice statistical mechanics, enumerative combinatorics,modular forms, modular equations, hypergeometric functions, orthogonal or symplectic differential Galois groups, series with integer coefficients, globally bounded series, differential equations Derived From Geometry, globally nilpotent operators, Calabi-Yau operators, Orphan Calabi-Yau operators, birational transformations.  

 

 



Mon sujet de thèse : Séries à coefficients entiers solutions d'équations différentielles linéaires et non linéaires en physique

Mon Directeur de thèse Jean Marie Maillard

 

ALGEBRAIC STATISTICAL MECHANICS

Diagonals of rational functions, Ising model, susceptibility of the Ising model, Yang-Baxter equations, Integrability, lattice statistical mechanics, enumerative combinatorics,modular forms, modular equations, hypergeometric functions, orthogonal or symplectic differential Galois groups, series with integer coefficients, globally bounded series, differential equations Derived From Geometry, globally nilpotent operators, Calabi-Yau operators, Orphan Calabi-Yau operators, birational transformations.  

 

Diagonales de Fonctions Rationnelles

Warm-up on diagonals :

  1. HDR de Bostan - COMPUTER ALGEBRA FOR LATTICE PATH COMBINATORICS
  2. Algebraic diagonals and walks: Algorithms, bounds, complexity 2015
  3. Differential algebra on lattice Green functions and Calabi–Yau operators  2014
  4. Ising n-fold integrals as diagonals of rational functions and integrality of series expansions: integrality versus modularity 2012
  5. Introduction simple sur les diagonales
  6. Diagonals of rational functions 2015
  7. Périodes d'intégrales rationnelles - Algorithmes et applications 2014
  8. Diagonals : Combinatorics, Asymptotics and Computer Algebra 2017
  9. Computer Algebra for Lattice Path Combinatorics I 2015
  10. Computer Algebra for Lattice Path Combinatorics II 2015
  11. Computer Algebra for Lattice Path Combinatorics III 2015

Simple example of diagonals of rational functions in physics: the Lattice Green functions

  1. Lattice Green functions: the d-dimensional face-centered cubic lattice, d = 8, 9, 10, 11, 12 2016
  2. Lattice Green's Functions of the Higher-Dimensional Face-Centered Cubic Lattices 
  3. Creative Telescoping 
  4. Computer algebra for Combinatorics (Hermite-Padé...)
  5. P-courbure 

Differentially algebraic series with integer coefficients

Warm-up on Differentially algebraic series with integer coefficients :

  1. Is the full susceptibility of the square-lattice Ising model a differentially algebraic function? 2016
  2. Selected non-holonomic functions in lattice statistical mechanics and enumerative combinatorics 2016
  3. Automata and the susceptibility of the square lattice Ising model modulo powers of primes 2015

 

Collaborations

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https://www.risc.jku.at/home/ckoutsch

Publications

 

  1. Diagonals of rational functions, pullbacked 2F1 hypergeometric functions and modular forms  2018
  2. Diagonals of rational functions, pullbacked 2F1 hypergeometric functions and modular forms (unabrigded version)  2018
  3. Modular forms, Schwarzian conditions, and symmetries of differential equations in physics 2017
  4. Schwarzian conditions for linear differential operators with selected differential Galois groups 2017
  5. Schwarzian conditions for linear differential operators with selected differential Galois groups (unabridged version) 2017

Contribution à un article dans le cadre de mon stage de Master 1

Science & Philosophie

Master 1 et 2 :  Logique, Philosophie, Histoire et Sociologie des Sciences, spécialité : Histoire et philosophie des mathématiques