# Dr Maxime Fairon

## Rankin-Sneddon Research Fellow

Room : 422

Address : School of Mathematics and Statistics, University of Glasgow, University Place, Glasgow, G12 8QQ

Email : Maxime . Fairon /AT/ glasgow . ac . uk

(Here is a short CV in English and my Academia profile)

From mid-January 2022, I am only working part-time at the University of Glasgow. I hold another part-time fellowship at Loughborough University.

#### Research Interests

• Poisson algebras
• Integrable systems and geometry
• Non-commutative Poisson geometry
• Double brackets

#### Papers and preprints

1. Morphisms of double (quasi-)Poisson algebras and action-angle duality of integrable systems.
Accepted in: Annales Henri Lebesgue (2022). arXiv:2008.01409

2. Superintegrability of Calogero-Moser systems associated with the cyclic quiver [with T.F. Görbe].
Nonlinearity 34, 7662--7682 (2021). URL ; arXiv:2101.05520

3. A decoupling property of some Poisson structures on $Mat_{n\times d}(\mathbb{C}) \times Mat_{d\times n}(\mathbb{C})$ supporting $GL(n,\mathbb{C}) \times GL(d,\mathbb{C})$ Poisson--Lie symmetry [with L. Fehér].
Journal of Mathematical Physics 62, 033512 (2021). URL; arXiv:2112.00381

4. Double quasi-Poisson brackets : fusion and new examples.
Algebras and Representation Theory 24, 911--958 (2021). URL ; arXiv:1905.11273

5. Trigonometric real form of the spin RS model of Krichever and Zabrodin [with L. Fehér, I. Marshall].
Annales Henri Poincaré 22, 615--675 (2021). URL ; arXiv:2007.08388

6. On the Hamiltonian formulation of the trigonometric spin Ruijsenaars-Schneider system [with O. Chalykh].
Letters in Mathematical Physics 110, 2893--2940 (2020). URL ; arXiv:1811.08727

7. Spin versions of the complex trigonometric Ruijsenaars-Schneider model from cyclic quivers.
Journal of Integrable Systems, Volume 4, Issue 1, xyz008 (2019). URL ; arXiv:1811.08717

8. Multiplicative quiver varieties and generalised Ruijsenaars-Schneider models [with O. Chalykh].
Journal of Geometry and Physics 121, 413-437 (2017). URL ; arXiv:1704.05814

European Journal of Mathematics 3 (2), 208-222 (2017). URL ; arXiv:1512.02810
• On the noncommutative Poisson geometry of certain wild character varieties [with D. Fernández]. arXiv:2103.10117

• Euler continuants in noncommutative quasi-Poisson geometry [with D. Fernández]. arXiv:2105.04858

• Integrable systems on multiplicative quiver varieties from cyclic quivers. arXiv:2108.02496

• Double Multiplicative Poisson Vertex Algebras [with D. Valeri]. arXiv:2110.03418

#### Thesis

• Multiplicative quiver varieties and integrable particle systems, University of Leeds (2019). Available here. (Supervisor : O. Chalykh)

#### Teaching

• MATHS4101 : Differential Geometry (2021-2022, Semester 2). See the Moodle page for more informations.
• MATHS4101 : Differential Geometry (2020-2021, Semester 2). See the Moodle page for more informations.
• MATHS4101 : Differential Geometry (2019-2020, Semester 2). See the Moodle page for more informations.

• Introduction to Integrability, Lecture Series (2020-2021, Semester 1).