I 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 2016 submitted my PhD thesis *On the global asymptotic analysis of a q-discrete Painlevé equation*. In my thesis I made effective the isomonodromic deformation method for the q-P(A_{1}) 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.

##### publications and preprints

Joshi, N. and Roffelsen, P. (2016) Analytic solutions of *q*–*P(A _{1})*near its critical points. Nonlinearity

**29**(3696).

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

Roffelsen, P. (2010) Irrationality of the Roots of the Yablonskii-Vorob’ev Polynomials and Relations between Them. *SIGMA*. **6**(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.

*Configuration of the roots in the complex plane of one of the generalised Okamoto polynomials. These polynomials are associated with rational solutions of the fourth Painlevé equation. Why these roots are so beautifully organised remains a mystery.*