Updated on 2025/04/03

写真a

 
STOKES, Alexander Henry
 
Affiliation
Affiliated organization, Waseda Institute for Advanced Study
Job title
Assistant Professor(non-tenure-track)

Research Experience

  • 2024.04
    -
    Now

    Waseda University   Institute for Advanced Study   Assistant Professor

  • 2023.12
    -
    2024.03

    University of Warsaw   Faculty of Mathematics, Informatics and Mechanics   Research Assistant Professor (adjunct)

  • 2021.11
    -
    2023.11

    The University of Tokyo   Graduate School of Mathematical Sciences   JSPS Overseas Research Fellow

  • 2021.05
    -
    2021.10

    London Mathematical Society   Early Career Fellow

    Hosted at the University of Warsaw and Loughborough University

Education Background

  • 2017.09
    -
    2020.09

    University College London   Faculty of Physical and Mathematical Sciences   Department of Mathematics  

    PhD in Mathematics

  • 2016.02
    -
    2016.11

    The University of Sydney   Faculty of Science   School of Mathematics and Statistics  

    Honours in Applied Mathematics

  • 2011.02
    -
    2015.11

    The University of Sydney   Faculty of Science  

    Bachelor of Science (Advanced Mathematics) and Bachelor of Arts (Major in Japanese Studies)

Professional Memberships

  • 2022.12
    -
    Now

    Japan Society for Industrial and Applied Mathematics

Research Areas

  • Mathematical analysis   Integrable Systems

Research Interests

  • orthogonal polynomials

  • delay-differential Painlevé equations

  • discrete Painlevé equations

  • Painlevé equations

  • integrable systems

 

Papers

▼display all

Presentations

  • Geometry of a four-dimensional multiplicative integrable mapping and associated fourth-order discrete Painlevé equations

    Alexander Stokes  [Invited]

    Joint Meeting of the New Zealand Mathematical Society, Australian Mathematical Society and American Mathematical Society 

    Presentation date： 2024.12

    Event date：
    2024.12
    　
    　

  • Geometry of a four-dimensional multiplicative integrable mapping and associated fourth-order discrete Painlevé equations

    Alexander Stokes

    Research meeting "From Nonlinear Waves to Integrable Systems 2024" 

    Presentation date： 2024.11

    Event date：
    2024.11
    　
    　

  • Geometry of a QRT-type mapping in four dimensions and associated q-discrete Painlevé equations

    Alexander Stokes  [Invited]

    Discrete Integrable Systems: Difference Equations, Cluster Algebras and Probabilistic Models 

    Presentation date： 2024.10

    Event date：
    2024.10
    -
    2024.11

  • Deautonomisation of integrable mappings and degree growth

    Alexander Stokes  [Invited]

    Elliptic Integrable Systems and Related Topics: Advanced Seminars (Shanghai University) 

    Presentation date： 2024.09

    Event date：
    2024.09
    　
    　

  • Geometric aspects of delay-differential Painlevé equations

    Alexander Stokes  [Invited]

    CNRS-Tokyo Workshop on 'Geometric Aspects of Painlevé Equations and Related Topics' 

    Presentation date： 2024.09

    Event date：
    2024.09
    　
    　

  • Roots of generalised Okamoto polynomials and partial-rogue waves in the Sasa-Satsuma equation

    Alexander Stokes  [Invited]

    Algebraic and Geometric Aspects of Differential and Difference Equations (University of Portsmouth) 

    Presentation date： 2024.06

    Event date：
    2024.06
    　
    　

  • Integrability and Geometry

    Alexander Stokes  [Invited]

    4PM Seminar, The Forefront Physics and Mathematics Program to Drive Transformation (FoPM), The University of Tokyo 

    Presentation date： 2024.06

  • Roots of generalised Okamoto polynomials and partial-rogue waves in the Sasa-Satsuma equation

    Alexander Stokes  [Invited]

    Nieliniowość i Geometria (Nonlinearity and Geometry) Seminar Faculty of Physics, University of Warsaw 

    Presentation date： 2024.02

  • On the zeroes of generalised Okamoto polynomials and singularity structure of real solutions of Painlevé-IV.

    Alexander Stokes

    Research meeting "From Nonlinear Waves to Integrable Systems 2023" 

    Presentation date： 2023.10

  • On the zeroes of generalised Okamoto polynomials and singularity structure of real solutions of Painlevé-IV

    Alexander Stokes  [Invited]

    Seminar of the TSVP Thematic Program "Exact Asymptotics: From Fluid Dynamics to Quantum Geometry" Okinawa Institute of Science and Technology (OIST) 

    Presentation date： 2023.10

  • Orthogonal polynomial ensembles and discrete Painlevé equations on the $D_5^{(1)}$ Sakai surface

    Alexander Stokes

    10th International Congress on Industrial and Applied Mathematics (ICIAM) Minisymposium on 'Painlevé equations, Applications, and Related Topics' 

    Presentation date： 2023.08

  • Orthogonal polynomial ensembles and discrete Painlevé equations on the $D_5^{(1)}$ Sakai surface

    Alexander Stokes  [Invited]

    Representation Theory, Integrable Systems and Related Topics Satellite conference of the First International Congress of Basic Science, Yanqi Lake Beijing Institute of Mathematical Sciences and Applications (BIMSA) 

    Presentation date： 2023.08

  • Full deautonomisation by singularity confinement as an integrability test: a geometric justification for birational mappings of the plane

    Alexander Stokes, Takafumi Mase, Ralph Willox, Basile Grammaticos

    ISLAND VI: Dualities and Symmetries in Integrable Systems 

    Presentation date： 2023.06

  • Full deautonomisation by singularity confinement as an integrability test

    Alexander Stokes

    SIDE14.2 International Conference on Symmetries and Integrability of Difference Equations 

    Presentation date： 2023.06

  • A beginner's guide to doing blow-ups on Painlevé equations

    Alexander Stokes  [Invited]

    Seminar of the Applied Mathematical Analysis Laboratory Graduate School of Informatics, Kyoto University 

    Presentation date： 2023.04

  • Full deautonomisation by singularity confinement as an integrability test for birational mappings of the plane

    Alexander Stokes, Takafumi Mase, Ralph Willox, Basile Grammaticos

    19th Research Group Joint Presentation Meeting of the Japan Society for Industrial and Applied Mathematics Organised Session of the Applied Integrable Systems Research Group 

    Presentation date： 2023.03

  • Geometric regularisation of a Hamiltonian system from a rational Calogero potential related to Painlevé-IV

    Alexander Stokes

    The Twelfth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory, Special Session on 'Discrete Painlevé Equations and Related Topics' 

    Presentation date： 2022.03

  • Geometric regularisation of a Hamiltonian system from a rational Calogero potential related to the fourth Painlevé equation

    Alexander Stokes  [Invited]

    School of Mathematics and Physics Colloquium, University of Portsmouth 

    Presentation date： 2021.11

  • Singularity confinement in delay-differential Painlevé equations

    Alexander Stokes  [Invited]

    Discrete Mathematical Modelling Seminar, Graduate School of Mathematical Sciences, The University of Tokyo 

    Presentation date： 2021.06

  • Identifying Painlevé equations related to orthogonal polynomials: the geometric approach

    Alexander Stokes  [Invited]

    OPSFOTA (Orthogonal Polynomials, Special Functions, Operator Theory and Applications) Seminar 

    Presentation date： 2021.05

  • What is an integrable difference equation?

    Alexander Stokes  [Invited]

    What is ... ? Seminar (WiSe), University of Queensland 

    Presentation date： 2021.03

  • Singularity confinement in delay-differential Painlevé equations

    Alexander Stokes  [Invited]

    FASnet20 Workshop (Formal and Analytic Solutions of Differential Equations on the Internet) 

    Presentation date： 2020.06

  • An introduction to the geometry of discrete Painlevé equations

    Alexander Stokes  [Invited]

    Analytic Theory of Differential Equations Seminar at the Banach Center, Mathematical Institute of the Polish Academy of Sciences 

    Presentation date： 2020.02

  • Why take the geometric approach to Painlevé equations?

    Alexander Stokes  [Invited]

    Dynamical Systems Seminar, Institute of Mathematics, University of Warsaw 

    Presentation date： 2019.12

  • Singularity confinement in delay-differential Painlevé equations - towards geometric interpretation

    Alexander Stokes

    ISLAND V: Integrable Systems, Special Functions and Combinatorics 

    Presentation date： 2019.06

  • Full-parameter discrete Painlevé systems from non-translational Cremona isometries

    Alexander Stokes

    SIDE13 International Conference on Symmetries and Integrability of Difference Equations 

    Presentation date： 2018.11

  • Full-parameter discrete Painlevé systems from non-translational Cremona isometries

    Alexander Stokes  [Invited]

    Aoyama Suri Seminar, Aoyama Gakuin University 

    Presentation date： 2018.11

  • Full-parameter discrete Painlevé systems from non-translational Cremona isometries

    Alexander Stokes

    Differential Algebra and Related Topics IX 

    Presentation date： 2018.08

▼display all

Research Projects

  • Extending the geometric theory of discrete Painleve equations beyond two dimensions

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2024.07
    -
    2026.03
     

  • Extending the geometric theory of discrete Painleve equations - singularities, entropy and integrability

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2023.03
    -
    2024.03
     

 

Syllabus

Teaching Experience

  • Advanced Mathematical Engineering

    Musashino University  

    2024.04
    -
    Now
     

 

Sub-affiliation

  • Faculty of International Research and Education   School of International Liberal Studies

Internal Special Research Projects

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

    2024   Anton Dzhamay, Takafumi Mase, Ralph Willox, Pieter Roffelsen, Yang Shi, Basile Grammaticos, Galina Filipuk, Michele Graffeo, Giorgio Gubbiotti

    　View Summary

    Painlevé equations, both differential and discrete, are nonlinear models in two dimensions with wide applications in mathematics and physics. Despite being nonlinear they are integrable (which, roughly speaking, means they exhibit ordered behaviour rather than chaos), and many of their properties can be understood through their association to a special class of geometric objects called generalised Halphen surfaces. This research fits within a broader program of extending this geometric framework, as well as the suite of tools it provides for the analysis of Painlevé equations, to both discrete Painlevé equations in higher dimensions and to delay-differential Painlevé equations, which are infinite-dimensional systems. The research conducted during the period funded by the grant has made significant progress on the geometry of higher-dimensional analogues of discrete Painlevé equations, geometric approaches to differential Painlevé equations appearing as higher-dimensional systems subject to some constraint, and related problems in the study of integrability and geometry more broadly. In particular, it has led to the establishment of the geometric structure of examples of multiplicative-type higher-dimensional discrete Painlevé equations for the first time. It has also led to insights into the algebraic structure of symmetries of discrete Painlevé equations, which will be used in further developing a geometric theory in higher dimensions. Some concrete research outputs of the project are listed below, including 2 published papers, 1 paper under review for publication, and 6 presentations at domestic and international conferences. The results obtained during the grant period have set a strong foundation for the continued pursuit of the research over the next years, and several more papers are in preparation.