Research

Preprints

• On real and imaginary roots of generalised Okamoto polynomials
  with Pieter Roffelsen. Submitted. https://arxiv.org/abs/2402.15887

• Full deautonomisation by singularity confinement as an integrability test
  with Takafumi Mase, Ralph Willox and Basile Grammaticos. Submitted. https://arxiv.org/abs/2306.01372

Journal Articles

• Delay Painlevé-I equation, associated polynomials and Masur-Veech volumes
  with John Gibbons and Alexander P. Veselov.
  Journal of Geometry and Physics 202 (2024), 105225.

• Orbifold Hamiltonian structures of certain quasi-Painlevé equations
  with Galina Filipuk.
  Journal of Dynamics and Differential Equations (2024), https://doi.org/10.1007/s10884-024-10352-z.

• Different Hamiltonians for differential Painlevé equations and their identification using a geometric approach
  with Anton Dzhamay, Galina Filipuk and Adam Ligȩza.
  Journal of Differential Equations 399 (2024), 281-334.

• On Hamiltonian structures of quasi-Painlevé equations
  with Galina Filipuk.
  Journal of Physics A: Mathematical and Theoretical 56 (2023), no. 49, 495205, 37pp.

• Takasaki's rational fourth Painlevé-Calogero system and geometric regularisability of algebro-Painlevé equations
  with Galina Filipuk.
  Nonlinearity 36 (2023), no. 10, 5661-5697.

• Differential equations for the recurrence coefficients of semi-classical orthogonal polynomials and their relation to the Painlevé equations via the geometric approach
  with Anton Dzhamay and Galina Filipuk.
  Studies in Applied Mathematics 148 (2022), no. 4, 1656-1702.

• On differential systems related to generalized Meixner and deformed Laguerre orthogonal polynomials
  with Anton Dzhamay and Galina Filipuk.
  Integral Transforms and Special Functions 32 (2021), no. 5-8, 483-492.

• Hamiltonian structure for a differential system from a modified Laguerre weight via the geometry of the modified third Painlevé equation
  with Anton Dzhamay, Galina Filipuk and Adam Ligȩza.
  Applied Mathematics Letters 120 (2021) 107248.

• Recurrence coefficients for discrete orthogonal polynomials with hypergeometric weight and discrete Painlevé equations
  with Anton Dzhamay and Galina Filipuk.
  Journal of Physics A: Mathematical and Theoretical 53 (2020), no. 49, 495201, 29pp.

• Singularity confinement in delay-differential Painlevé equations
  Journal of Physics A: Mathematical and Theoretical 53 (2020), no. 43, 435201, 31pp.

• Full-parameter discrete Painlevé systems from non-translational Cremona isometries
  Journal of Physics A: Mathematical and Theoretical 51 (2018), no. 49, 495206, 31pp.

Refereed Proceedings

• Relations between different Hamiltonian forms of the third Painlevé equation
  with Galina Filipuk and Adam Ligȩza.
  in Recent Trends in Formal and Analytic Solutions of Diff. Equations,
  Contemp. Math. 782, Amer. Math. Soc., Providence, RI, 2023.

• On Hamiltonians related to the second Painlevé equation
  with Anton Dzhamay, Galina Filipuk and Adam Ligȩza.
  Proceedings of the conference Contemporary Mathematics in Kielce 2020, Jan Kochanowski University in Kielce, Poland, (2021), 74-84.

Thesis

• Studies on the geometry of Painlevé equations
  Doctoral thesis (Ph.D.), UCL (University College London), 2020.