CASA, the Center for Analysis, Scientific Computing, and Applications is one of three sections of the Division of Mathematics, in addition to the sections Discrete Mathematics and Stochastics. The major research objective of CASA is to develop and improve mathematical methods (both analytical and numerical) inspired by a wide range of applications in science and engineering. There are three subgroups: the Applied Analysis group mainly focuses on qualitative properties of solutions of partial differential equations; the Scientific Computing group concentrates on development and analysis of numerical methods; and the Mathematical Image Analysis group focuses on design and implementation of algorithms for the analysis and manipulation of images.

Project description

Evolution equations in spaces of measures describe a wide variety of natural phenomena. The theory for such evolutions has seen tremendous growth in the last decades, of which resulted in Ambrosio-Gigli-Savaré (AGS) and rate independent (RI) theory for analyzing variational evolutions—evolutions driven by one or more energies/entropies. The AGS theory provides a rich framework to study gradient flows in general metric spaces, where the Wasserstein metric of optimal transport theory plays a fundamental role in the case of probability measures. The aim of this project is to develop a theory for dynamical-variational transport costs (DVTs), a class of large-deviation inspired functionals that provide a variational generalization of several existing transport distances. Since DVTs generate non-homogeneous generalizations of length spaces and are stable under weak convergence, they will be used to extend metric-space techniques to general length spaces, thereby allowing a variational framework for (1) generalized gradient flows to be rigorously investigated, and (2) the multiscale analysis of such evolutions used in the development of numerical schemes.

The project is part of an NWO VIDI project, and will consist of two PhD students and the supervisor himself. Together with the supervisor, one student will focus on establishing well-posedness of a class of nonlocal equations arising from Lévy processes by means of DVTs, while the other student will be involved in the development of mimetic numerical schemes for Wasserstein gradient flows that are adapted to the space of measures. Since the supervisor will be heavily involved in the research, there will be close interaction and collaboration among the PhD students and the supervisor.

We are looking for a candidate that meets the following requirements:

The successful applicant should hold a Master's degree in Mathematics, Applied Mathematics or related fields;

Strong knowledge of calculus of variations, and functional analysis is highly desirable;

An interest in cross-topic collaboration between different fields of mathematics;

Affinity with high-level, mathematics oriented programming languages (Matlab, Python, etc.);

Good communicative skills in English, both in speaking and in writing;

Candidates from non-Dutch or non-English speaking countries should be prepared to prove their English language skills

We offer:

A challenging job in a dynamic and ambitious University, and a stimulating research environment;

Full-time employment as a PhD-candidate for a period of 4 years;

A gross salary of € 2.222 per month in the first year increasing up to € 2.840 in the fourth year;

Annually 8% holiday allowance and 8.3% end of year allowance;

Support with your personal development and career planning including courses, summer schools, conference visits etc.;

An extensive package of fringe benefits (e.g. support in moving expenses and commuting expenses, excellent technical infrastructure, on-campus child care, and excellent sports facilities, extra holiday allowance (8%, May), and end-of-year bonus (8.3%, December)).