Waseda Institute for Advanced Study (WIAS)早稲田大学 高等研究所

名前

ストークス　アレクサンダー（STOKES, Alexander）

取得学位

Ph.D. in Mathematics

HP (URL)

https://sites.google.com/view/alexanderstokes

資格

講師

研究テーマ

Extending the geometric theory of discrete Painlevé equations to higher and infinite dimensions

私の研究は、「非線形可積分系」という数理モデルの解明を目的としている。一般の非線形の場合とは対照的に、可積分系の振る舞いにはカオスが起こらず、豊富な対称性を持つ。多くの場合にこれは幾何学的な構造の存在で解釈できる。現在の研究は「パンルヴェ方程式」という二次元可積分系を中心として、それを記述する幾何学的な理論を高次元及び無限次元パンルヴェ方程式へ拡張しようとするものである。

Monthly Spotlight

[Monthly Spotlight]は研究員にスポットをあて、研究内容とそのビジョンを毎月紹介していくコンテンツです。
Integrability, geometry and mathematical phenomenology

略歴

学歴

職歴

研究項目

可積分系、パンルヴェ方程式、離散パンルヴェ方程式、遅延型パンルヴェ方程式、数理物理学、双有理写像の可積分性

主な研究業績

[Journal articles]

• A. Dzhamay, G. Filipuk and A. Stokes, “On the discrete Painlevé equivalence problem, non-conjugate translations and nodal curves”, Letters in Mathematical Physics 116 (2026), no. 4, 96, 49pp.
• P. Roffelsen and A. Stokes, “On real and imaginary roots of generalised Okamoto polynomials”, Journal of the London Mathematical Society 112 (2025), no. 4, e70329, 69pp.
• A. Stokes, T. Takenawa and A. S. Carstea, “On the geometry of a 4-dimensional extension of a q-Painlevé I equation with symmetry type A_1^{(1)}”, Journal of Physics A: Mathematical and Theoretical 58 (2025), no. 40, 405201, 30pp.
• A. Dzhamay, Y. Shi, A. Stokes and R. Willox, “What is the symmetry group of a d-PII discrete Painlevé equation?”, Mathematics 13 (2025), no. 7, article number 1123, 28pp.
• 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 polynomi als and Masur-Veech volumes”, Journal of Geometry and Physics 202 (2024), 105225, 24pp.
• A. Dzhamay, G. Filipuk, A. Ligęza and A. Stokes, “Different Hamiltonians for differential Painlevé equations and their identification using a geometric approach”, Journal of Differential Equations 399 (2024), 281-334.
• G. Filipuk and A. Stokes, “Orbifold Hamiltonian structures of certain quasi-Painlevé equations”, Journal of Dynamics and Differential Equations (2024) 37 (2024), 2323-2340.
• G. Filipuk and A. Stokes, “On Hamiltonian structures of quasi-Painlevé equations”, Journal of Physics A: Mathematical and Theoretical 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, 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”, Studies in Applied Mathematics 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 Special Functions 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”, Applied Mathematics Letters 120 (2021), 107248. 7pp.
• A. Dzhamay, G. Filipuk and A. Stokes, “Recurrence coefficients for discrete orthogonal polynomials with hypergeometric weight and discrete Painlevé equations”, Journal of Physics A: Mathematical and Theoretical 53 (2020), no. 49, 495201, 29pp.
• A. Stokes, “Singularity confinement in delay-differential Painlevé equations”, Journal of Physics A: Mathematical and Theoretical 53 (2020), no. 43, 435201, 31pp.
• A. Stokes, “Full-parameter discrete Painlevé systems from non-translational Cremona isometries”, Journal of Physics A: Mathematical and Theoretical 51 (2018), no. 49, 495206, 31pp.

[Book chapters]

• G. Alecci, M. Graffeo and A. Stokes, “Classical algebraic geometry and discrete integrable systems”, in Symmetries and Integrability of Difference Equations, Contemporary Mathematics 847, pp. 1-81, American Mathematical Society, Providence RI, 2026

[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, Contemporary Mathematics 782, pp. 37-42. American Mathematical Society, Providence RI, 2026
• 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.

趣味 関心

音楽、サイクリング, 建築、海

所属学会

日本応用数理学会

受賞歴

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)