PhD candidate for mathematics

Employer
KU Leuven
Location
Europe
Posted
September 14 2017
Position Type
Full Time
Organization Type
Academia

The Analysis Section of the Departement of Mathematics and the Departement of Mathematics of Radboud University in The Netherlands are seeking an outstanding, highly motivated PhD candidate to work on a project called `Matrix-valued Special Functions and Applications in Physics'. The project concerns the area of analysis, more particularly special functions, with applications in physics. The project is funded by Radboud University and KU Leuven; you will work at each of these two universities for two years. The project is part of a larger programme strengthening the ties between Radboud University and KU Leuven and is supervised by Prof. Erik Koelink (Radboud University) and Prof. Walter Van Assche (KU Leuven).

Upon successful completion, you will be awarded a PhD from both Radboud University and KU Leuven. You will be encouraged to attend and contribute to international scientific meetings. You will have a light teaching load and, if necessary, you will be required to perform your teaching duties in English. You will be based at the Department of Mathematics at Radboud University during the first two years. The Department of Mathematics is part of the Institute for Mathematics, Astrophysics and Particle Physics (IMAPP). IMAPP has a friendly and open atmosphere, and a strong expertise in mathematical physics and analysis. This year, for the third time in the past five years, our mathematics programme received the highest undergraduate student ratings in a national student survey.

You will be based at the Department of Mathematics at KU Leuven during the last two years of the project. The Department of Mathematics is part of the Faculty of Sciences at KU Leuven. You will work in the Section of Analysis, which has two research groups, one in Classical Analysis (CA) and one in Functional Analysis (FA), with many national and international researchers at the graduate and postdoctoral levels.


The research project is called 'Matrix-valued Special Functions and Applications in Physics' and concerns the area of analysis, more particularly special functions, with applications in physics. 


The main work packages in the project are:


- Using explicit families and deformation strategies to find solutions to matrix Toda lattices and related hierarchies, including Lax pair formulations and boundary conditions. We start using recently established sets of matrix-valued orthogonal polynomials, using the fact that we can introduce the time dependence in different ways using the non-commutativity.

- Study the asymptotic behaviour of the deformed polynomials and the recursion coefficients using the Riemann-Hilbert approach extension to matrix-valued orthogonal polynomials. Establish a connection to inverse scattering.

- Relate to solutions of matrix Painlevé equations using the previous results and determine the corresponding Bäcklund transformations. Investigate the corresponding symmetries.



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