Pieter Roffelsen

Pieter Roffelsen by Ted SealeyI am a research associate in the integrable systems group headed by Prof. Nalini Joshi at The University of Sydney.

I am interested in the global asymptotic analysis of discrete and continuous Painlevé equations, which involves:
– classifying critical behaviour of solutions near critical points,
– solving the corresponding connection problem, and
– finding the distribution of special points such as zeros and poles.

Recently I have been collaborating with Dr Davide Masoero, on the distribution of special points of Painlevé IV rationals and their relation to finite families of Nevanlinna functions.

In the beginning of 2017 I received my doctorate in mathematics from the university of Sydney, with Nalini Joshi as my supervisor. In my PhD thesis On the global asymptotic analysis of a q-discrete Painlevé equation, I made effective the isomonodromic deformation method for the q-P(A1) equation, which is an 8-parameter generalisation of the sixth Painlevé equation. In particular I explicitly related the generic critical behaviour of solutions to monodromy of an associated linear problem.

In 2012 I completed my MSc in Mathematics at Radboud University in Nijmegen. During my masters degree, I studied rational solutions of the fourth  Painlevé equation under the supervision of Prof P.A. Clarkson and Prof H.T. Koelink.

Rescaled roots of generalised Hermite polynomial H40,5. In blue numerically exact location, in red the asymptotic approximation and in purple the curves on which they condensate, as worked out in my recent paper with Davide Masoero.
publications and preprints

Masoero, D. and P. Roffelsen (2017) Poles of Painlevé IV Rationals and their Distribution. In pre-print.

Joshi, N. and Roffelsen, P. (2016) Analytic solutions of qP(A1)near its critical points. Nonlinearity 29(3696).

Roffelsen, P. (2012) On the Number of Real Roots of the Yablonskii-Vorob’ev PolynomialsSIGMA. 8(099): 9 pages.

Roffelsen, P. (2010) Irrationality of the Roots of the Yablonskii-Vorob’ev Polynomials and Relations between Them. SIGMA6(095): 11 pages

TRAVEL IN 2017

February: Visiting Davide Masoero at the University of Lisbon.
Asymptotic and computational aspects of complex differential equations in Pisa, Italy.

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