LABORATOIRE J.A. DIEUDONNE UMR CNRS-UNS N°7351

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THEMES DE RECHERCHE

• Algèbres de Hopf (graphes de Feynman, méthodes perturbatives)/ Hopf algebras (Feynman graphs, perturbative expansions)
• Calcul moulien et Combinatoire des systèmes dynamiques / Mould Calculus and Combinatorics of dynamical systems
  
• Chimie quantique/ Quantum chemistry
• Méthodes numériques (Monte Carlo)/Numerical methods (Monte Carlo)
  
• Théorie quantique des champs/ QFT
  

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ARTICLES EN CHIMIE QUANTIQUE/PHYSIQUE
 (WARNING: PREPRINT VERSIONS MAY DIFFER FROM PUBLISHED ONES)

With R. Chétrite, Algebraic structures underlying quantum independences : Theory and Applications, Ann. Henri Poincaré 25, 253–296 (2024).

With R. Chétrite, Les structures algébriques de l'aléatoire, du classique au quantique. In Informatique mathématique. Une photographie en 2022, B. Martin et al. eds, CNRS Editions, 2022, 245--292.

With Patrick Cassam-Chenai, Guillaume Dhont Molien functions and generalized integrity bases for SO(3) and related groups. J. Math Chem (59) 2021 2294-2326.

With F. Menous, Renormalization: a quasi-shuffle approach. Computation and Combinatorics in Dynamics, Stochastics and Control: The Abel Symposium 2016. Celledoni, E. et al. Springer (2018), pp. 599-628.

With Frédéric Menous, Right-handed bialgebras and the Prelie forest formula. Annales I.H.P. Série D, Volume 5, Issue 1, 2018, 103-125..

With K. Ebrahimi-Fard, The combinatorics of Green's functions in planar field theories. Front. Phys. 11(6), 110310 (2016).

With K. Ebrahimi-Fard, S.J.A. Malham and A. Wiese, The exponential Lie series for continuous semimartingales. Proc. R. Soc. A 2015 471 20150429.

With K. Ebrahimi-Fard, S.J.A. Malham and A. Wiese, Flows and stochastic Taylor series in Ito calculus. J. Phys. A: Math. Theor. 48 (2015) 495202.

With Guillaume Dhont and Boris Zhilinskii, The action of the special orthogonal group on planar vectors: integrity bases via a generalization of the symbolic interpretation of Molien functions, J. Phys. A: Math. Theor. 48 (2015) 035201.

With Patrick Cassam-Chenaï and Guillaume Dhont, A Fast Algorithm for the Construction of Integrity Bases Associated to Symmetry-Adapted Polynomial Representations. Application to Tetrahedral XY4 Molecules. Journal of Mathematical Chemistry: Volume 53, Issue 1 (2015), Page 58-85

With K. Ebrahimi-Fard, The preLie structure of the time-ordered exponential. Lett. Math. Phys. (2014), 104, 1281–1302.

With M. Bauer, R. Chetrite and K. Ebrahimi-Fard Time-ordering and a generalized Magnus expansion Letters Math. Phys. (2013), 103 (3), 331-350.

With K. Ebrahimi-Fard Exponential Renormalization II: Bogoliubov's R-operation and momentum subtraction schemes J. Math. Phys. 53, 083505 (2012)

With Ch. Brouder, G. Duchamp and G. Z. Toth. The Rayleigh-Schrödinger perturbation series of quasi-degenerate systems. Int. J. Quantum Chem. Volume 112, Issue 10 (2012) Pages: 2256–2266.

With Ch. Brouder. Nonlocal, noncommutative diagrammatics and the linked cluster Theorems J. Math. Chem. (2012) Volume 50, Number 3, Pages 552-576

With Ch. Brouder. One-particle irreducibility with initial correlations. Combinatorics and Physics Eds Ebrahimi-Fard, Marcolli, van Suijlekom, Contemporary Mathematics Vol. 539, (2011), 1--25.

With K. Ebrahimi-Fard. Exponential renormalization. Annales Henri Poincaré 11 (5), (2010), 943--971.

With Ch. Brouder and A. Mestre. Tree expansions in time-dependent perturbation theory. J. Math. Phys. 51, 072104/1-25 (2010)

With Ch. Brouder. Hyperoctahedral Chen calculus for effective Hamiltonians. J. Algebra 322 (2009), 4105-4120.

Dynkin operators and renormalization group actions in pQFT. in: Vertex Operator Algebras and Related Areas, Eds M. Bergvelt, G. Yamskulna, W. Zhao, Contemp. Math. vol. 497 (2009), 169-184.

With P. Del Moral and S. Rubenthaler. Tree based functional expansions for Feynman-Kac particle models . Annals of Applied Probability Vol. 19, No. 2, 778–825 (2009)

With K. Ebrahimi-Fard and D. Manchon. A noncommutative Bohnenblust-Spitzer identity for Rota-Baxter algebras solves Bogolioubov's recursion . Journal of Noncommutative Geometry , Vol. 3, Issue 2 (2009), 181-222.

With P. Cassam-Chenai. Symmetry-Adapted Polynomial Basis for Global Potential Energy Surfaces - Applications to XY4 Molecules . J. Math. Chem. 44, 938-966, (2008)

With K. Ebrahimi-Fard. A Zassenhaus-type algorithm solves the Bogoliubov recursion. Bulgarian J. of Physics. Lie Theory and its Applications in Physics VII, 35 (s1), 303-315 (2008)

With K. Ebrahimi-Fard and J. Gracia-Bondia. A Lie theoretic approach to renormalization . Comm. Math. Phys. 276, 519-549 (2007)

With K. Ebrahimi-Fard and J. Gracia-Bondia. Rota-Baxter algebras and new combinatorial identities. Letters in Math. Physics 81, (1), (2007), 61-75.

With P. Cassam-Chenai. Higher order, generalized, Schmidt decompositions for indistinguishable, overlapping particles. Physics Letters A. Vol 326/5-6, (2004), 297-306.

With P. Cassam-Chenai. The Hopf algebra of identical, fermionic particle systems - fundamental concepts and properties. J. Math. Phys. 44, (11), (2003), 4884-4906.

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