The candidate holds a master degree in mathematics or mathematical engineering or equivalent programme, is interested in mathematical research in an academic environment and aims for obtaining a PhD degree.Polynomials are ubiquitous in analysis and scientific computing, while rational functions are equally foundational but relatively unexplored in comparison. Advances in the past five to ten years have resulted in great strides forward both in numerical tools and in applicability of rational functions of a single variable. It is the goal of the project to make another leap forward, by building tools for rational functions of several variables. Solving the strongly nonlinear problem of best approximation using multivariate rational functions is highly challenging and would be transformative across disciplines. The project identifies several paths towards that ambitious goal, each within the joined expertise of the PIs, with progressive levels of complexity. Specific research goals focus...