Research
Research
On the geometry of a 4-dimensional extension of a q-Painlevé I equation with symmetry type A_1^{(1)}
with Tomoyuki Takenawa and Adrian Stefan Carstea. https://arxiv.org/abs/2506.21092
The Painlevé equivalence problem for a constrained 3D system
with Galina Filipuk, Michele Graffeo and Giorgio Gubbiotti. https://arxiv.org/abs/2411.01657
On real and imaginary roots of generalised Okamoto polynomials
with Pieter Roffelsen. https://arxiv.org/abs/2402.15887
(13) What is the symmetry group of a d-PII discrete Painlevé equation?
with Anton Dzhamay, Yang Shi and Ralph Willox.
Mathematics 13 (2025), no. 7, article number 1123, 28pp.
Special Issue on "Advanced Research in Mathematical Physics with Painlevé Property and Affine Weyl Group Symmetry", Special Issue Editor Prof. Dr. Henrik Aratyn (University of Illinois at Chicago).
(12) Deautonomisation by singularity confinement and degree growth
with Takafumi Mase, Ralph Willox and Basile Grammaticos.
Journal of Geometric Analysis 35 (2025), article number 65, 63pp.
(11) 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.
(10) 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.
(9) 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.
(8) On Hamiltonian structures of quasi-Painlevé equations
with Galina Filipuk.
Journal of Physics A: Mathematical and Theoretical 56 (2023), no. 49, 495205, 37pp.
(7) Takasaki's rational fourth Painlevé-Calogero system and geometric regularisability of algebro-Painlevé equations
with Galina Filipuk.
Nonlinearity 36 (2023), no. 10, 5661-5697.
(6) 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.
(5) 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.
(4) 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.
(3) 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.
(2) Singularity confinement in delay-differential Painlevé equations
Journal of Physics A: Mathematical and Theoretical 53 (2020), no. 43, 435201, 31pp.
(1) Full-parameter discrete Painlevé systems from non-translational Cremona isometries
Journal of Physics A: Mathematical and Theoretical 51 (2018), no. 49, 495206, 31pp.
(2) 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.
(1) 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.
Studies on the geometry of Painlevé equations
Doctoral thesis (Ph.D.), UCL (University College London), 2020.