Name
STOKES, Alexander
Degree
Ph.D. in Mathematics
HP (URL)
https://sites.google.com/view/alexanderstokes
Status
Assistant Professor
Research Topic
Extending the geometric theory of discrete Painlevé equations to higher and infinite dimensions
My research seeks to understand a class of mathematical models known as nonlinear integrable systems. While nonlinearity generally leads to chaos, integrable systems exhibit regular behaviour and an abundance of symmetry, which can in many cases be explained in terms of some underlying geometric structure. My current work aims to extend the geometric picture for a class of integrable systems in two-dimensions, called Painlevé equations, to analogous systems in higher and infinite dimensions.
Monthly Spotlight
[Monthly Spotlight] is focusing on a researcher to introduce his/her research.
Integrability, geometry and mathematical phenomenology
Education and Academic Employment
Education
| 2017-2020 | University College London (PhD in Mathematics) |
| 2016 | The University of Sydney, School of Mathematics and Statistics (Honours in Applied Mathematics) |
| 2011-2015 | The University of Sydney (Bachelor of Science (Advanced Mathematics) and Bachelor of Arts (Major in Japanese Studies)) |
Academic Employment
| 2023-2024 | Warsaw University, Faculty of Mathematics, Informatics and Mechanics, Research Assistant Professor (adjunct) |
| 2021-2023 | The University of Tokyo, Graduate School of Mathematical Sciences, JSPS Fellow |
| 2021 | London Mathematical Society Early Career Fellow, hosted at Loughborough University and University of Warsaw |
| 2020-2021 | King’s College London, Department of Mathematics, External Teaching Assistant |
| 2017-2021 | University College London, Department of Mathematics, Graduate Tutor/Demonstrator |
Fields of Research Interests
Integrable systems, Painlevé equations, discrete Painlevé equations, delay-differential Painlevé equations, mathematical physics, integrability of birational mappings
Academic Publications
[Journal articles]
- A. Stokes, T. Mase, R. Willox and B. Grammaticos, “Deautonomisation by singularity confinement and degree growth”, Journal of Geometric Analysis 35 (2025), article number 65, 63pp.
- J. Gibbons, A. Stokes and A. P. Veselov, “Delay Painlevé-I equation, associated polynomials and Masur-Veech volumes”, J. Geom. Phys. 202 (2024), 105225.
- A. Dzhamay, G. Filipuk, A. Ligęza and A. Stokes, “Different Hamiltonians for differential Painlevé equations and their identification using a geometric approach”, J. Differential Equations 399 (2024), 281-334.
- G. Filipuk and A. Stokes, “Orbifold Hamiltonian structures of certain quasi-Painlevé equations”, J. Dynam. Differential Equations (2024)
- G. Filipuk and A. Stokes, “On Hamiltonian structures of quasi-Painlevé equations”, J. Phys. A: Math. Theor. 56 (2023), no. 49, 495205, 37pp.
- G. Filipuk and A. Stokes, “Takasaki’s rational fourth Painlevé-Calogero system and geometric regularisability of algebro-Painlevé equations”, Nonlinearity 36 (2023), no. 10, no. 10, 5661-5697.
- A. Dzhamay, G. Filipuk and A. Stokes, “Differential equations for the recurrence coefficients of semi-classical orthogonal polynomials and their relation to the Painlevé equations via the geometric approach”, Stud. Appl. Math. 148 (2022), no. 4, 1656-1702.
- A. Dzhamay, G. Filipuk and A. Stokes, “On differential systems related to generalized Meixner and deformed Laguerre orthogonal polynomials”, Integral Transforms Spec. Funct. 32 (2021), no. 5-8, 483-492.
- A. Dzhamay, G. Filipuk, A. Ligęza and A. Stokes, “Hamiltonian structure for a differential system from a modified Laguerre weight via the geometry of the modified third Painlevé equation”, Appl. Math. Lett. 120 (2021), 107248.
- A. Dzhamay, G. Filipuk and A. Stokes, “Recurrence coefficients for discrete orthogonal polynomials with hypergeometric weight and discrete Painlevé equations”, J. Phys. A: Math. Theor. 53 (2020), no. 49, 495201, 29pp.
- A. Stokes, “Singularity confinement in delay-differential Painlevé equations”, J. Phys. A: Math. Theor. 53 (2020), no. 43, 435201, 31pp.
- A. Stokes, “Full-parameter discrete Painlevé systems from non-translational Cremona isometries”, J. Phys. A: Math. Theor. 51 (2018), no. 49, 495206, 31pp.
[Refereed proceedings]
- G. Filipuk, A. Ligęza and A. Stokes, “Relations between different Hamiltonian forms of the third Painlevé equation”, in Recent Trends in Formal and Analytic Solutions of Diff. Equations, Contemp. Math. 782, Amer. Math. Soc., 2023.
- A. Dzhamay, G. Filipuk, A Ligęza and A. Stokes, “On Hamiltonians related to the second Painlevé equation”, Proceedings of the conference Contemporary Mathematics in Kielce 2020, Jan Kochanowski University in Kielce, Poland, (2021), 74-84.
Other Interests
Music, cycling, architecture, the ocean
Affiliated Academic Organizations
Japan Society for Industrial and Applied Mathematics
Awards
2019 : Andrew Rosen Prize (awarded by Department of Mathematics, University College London)
2018 : Sir George Jessel Studentship (awarded by Department of Mathematics, University College London)
2018 : Poster Presentation Prize of the SIDE13 International Conference on Symmetries and Integrability of Difference Equations
2015 : K. E. Bullen Scholarship II in Applied Mathematics (awarded by School of Mathematics and Statistics, The University of Sydney)
2014 : Mark Kwan Memorial Prize for Japanese Studies (awarded School of Languages and Cultures, The University of Sydney)
