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I am interested in the relations that exist between algebraic and geometric structures in the context of integrable systems. In particular, I study the non-commutative versions of Poisson geometry defined on associative algebras in order to find new classes of integrable systems on the representation spaces associated to these algebras.
Fairon, M. and Valeri, D. (2023) Double multiplicative Poisson vertex algebras. International Mathematics Research Notices, 2023(17), pp. 14991-15072. (doi: 10.1093/imrn/rnac245)
Fairon, M. and McCulloch, C. (2023) Around Van den Bergh’s double brackets for different bimodule structures. Communications in Algebra, 51(4), pp. 1673-1706. (doi: 10.1080/00927872.2022.2140349)
Fairon, M. (2022) Morphisms of double (quasi-)Poisson algebras and action-angle duality of integrable systems. Annales Henri Lebesgue, 5, pp. 179-262. (doi: 10.5802/ahl.121)
Fairon, M. and Fernández, D. (2022) Euler continuants in noncommutative quasi-Poisson geometry. Forum of Mathematics, Sigma, 10, e88. (doi: 10.1017/fms.2022.76)
Fairon, M. (2021) Double quasi-Poisson brackets: fusion and new examples. Algebras and Representation Theory, 24(4), pp. 911-958. (doi: 10.1007/s10468-020-09974-w)
Fairon, M. and Fehér, L. (2021) A decoupling property of some Poisson structures on Matn×d(C)×Matd×n(C) supporting GL(n,C)×GL(d,C) Poisson–Lie symmetry. Journal of Mathematical Physics, 62(3), 033512. (doi: 10.1063/5.0035935)
Fairon, M. , Fehér, L. and Marshall, I. (2021) Trigonometric real form of the spin RS model of Krichever and Zabrodin. Annales Henri Poincaré, 22(2), pp. 615-675. (doi: 10.1007/s00023-020-00976-4)
Fairon, M. and Görbe, T. (2021) Superintegrability of Calogero-Moser systems associated with the cyclic quiver. Nonlinearity, 34(11), pp. 7662-7682. (doi: 10.1088/1361-6544/ac2674)
Chalykh, O. and Fairon, M. (2020) On the Hamiltonian formulation of the trigonometric spin Ruijsenaars-Schneider system. Letters in Mathematical Physics, 110(11), pp. 2893-2940. (doi: 10.1007/s11005-020-01320-x)
Fairon, M. (2019) Spin versions of the complex trigonometric Ruijsenaars-Schneider model from cyclic quivers. Journal of Integrable Systems, 4(1), xyz008. (doi: 10.1093/integr/xyz008)
Chalykh, O. and Fairon, M. (2017) Multiplicative quiver varieties and generalised Ruijsenaars–Schneider models. Journal of Geometry and Physics, 121, pp. 413-437. (doi: 10.1016/j.geomphys.2017.08.006)
Fairon, M. (2017) Introduction to graded geometry. European Journal of Mathematics, 3(2), pp. 208-222. (doi: 10.1007/s40879-017-0138-4)
Fairon, M. and Valeri, D. (2023) Double multiplicative Poisson vertex algebras. International Mathematics Research Notices, 2023(17), pp. 14991-15072. (doi: 10.1093/imrn/rnac245)
Fairon, M. and McCulloch, C. (2023) Around Van den Bergh’s double brackets for different bimodule structures. Communications in Algebra, 51(4), pp. 1673-1706. (doi: 10.1080/00927872.2022.2140349)
Fairon, M. (2022) Morphisms of double (quasi-)Poisson algebras and action-angle duality of integrable systems. Annales Henri Lebesgue, 5, pp. 179-262. (doi: 10.5802/ahl.121)
Fairon, M. and Fernández, D. (2022) Euler continuants in noncommutative quasi-Poisson geometry. Forum of Mathematics, Sigma, 10, e88. (doi: 10.1017/fms.2022.76)
Fairon, M. (2021) Double quasi-Poisson brackets: fusion and new examples. Algebras and Representation Theory, 24(4), pp. 911-958. (doi: 10.1007/s10468-020-09974-w)
Fairon, M. and Fehér, L. (2021) A decoupling property of some Poisson structures on Matn×d(C)×Matd×n(C) supporting GL(n,C)×GL(d,C) Poisson–Lie symmetry. Journal of Mathematical Physics, 62(3), 033512. (doi: 10.1063/5.0035935)
Fairon, M. , Fehér, L. and Marshall, I. (2021) Trigonometric real form of the spin RS model of Krichever and Zabrodin. Annales Henri Poincaré, 22(2), pp. 615-675. (doi: 10.1007/s00023-020-00976-4)
Fairon, M. and Görbe, T. (2021) Superintegrability of Calogero-Moser systems associated with the cyclic quiver. Nonlinearity, 34(11), pp. 7662-7682. (doi: 10.1088/1361-6544/ac2674)
Chalykh, O. and Fairon, M. (2020) On the Hamiltonian formulation of the trigonometric spin Ruijsenaars-Schneider system. Letters in Mathematical Physics, 110(11), pp. 2893-2940. (doi: 10.1007/s11005-020-01320-x)
Fairon, M. (2019) Spin versions of the complex trigonometric Ruijsenaars-Schneider model from cyclic quivers. Journal of Integrable Systems, 4(1), xyz008. (doi: 10.1093/integr/xyz008)
Chalykh, O. and Fairon, M. (2017) Multiplicative quiver varieties and generalised Ruijsenaars–Schneider models. Journal of Geometry and Physics, 121, pp. 413-437. (doi: 10.1016/j.geomphys.2017.08.006)
Fairon, M. (2017) Introduction to graded geometry. European Journal of Mathematics, 3(2), pp. 208-222. (doi: 10.1007/s40879-017-0138-4)
4H : Differential Geometry
https://orcid.org/0000-0002-2787-6913