Systems with multiple time- or spatial scales are ubiquitous in the natural sciences and beyond. For example such systems are studied in statistical physics, finance, atmospheric models and appear in the theory for molecular motors.
In the mathematical study of such systems, we look at the behaviour of the systems in the limit where one of the fast, or microscopic parameters, is averaged out. The study of these limits is challenging as the effective result of the averaged components need to be combined with the slow, or macroscopic, components of the system.

In this project, we will study the large deviations of stochastic multi-scale systems. Large deviation theory is a tool that allows one to quantify not only the limit of the system as the scale separation goes to infinity, but also which behaviours have a relatively large probability to appear at finite scale separation.

As a key technical tool, we will study a collection of associated fully non-linear partial differential equations called Hamilton-Jacobi-Bellman equations using viscosity methods. We will consider both existence and uniqueness theory for this highly challenging class of equations.

The research work for the prospective PhD candidate lies in the intersection of the area of theoretical probability (Markov processes and large deviations) and non-linear PDE's (Hamilton-Jacobi equations, and control theory).
In addition to the research work, the student is expected to make a small contribution (10% of the work load) to teaching. This usually consists of leading exercise classes for Bachelor or Master courses in mathematics.

Department
Research at the Delft Institute of Applied Mathematics (DIAM) centres around the analysis of mathematical models arising in science and engineering. This research is both fundamental and applied in nature, and is often inspired by technical applications. The department plays an active role in translating research results into concrete, practical applications. It maintains intensive contacts with other TU Delft departments, the major technological institutes, and the research laboratories of major companies. Within its own subject field, the department provides teaching for the Applied Mathematics BSc and MSc programmes, and also contributes to the teaching of mathematics courses within other academic programmes at the TU Delft and within national programmes such as “MasterMath”.
The Delft Institute of Applied Mathematics consists of six research groups: Analysis, Mathematical Physics, Numerical Analysis, Applied Probability, Statistics, and Optimisation.

1. A MSc degree in mathematics with specialisation in the area of theoretical probability or analysis
2. Good communication skills both in written and spoken English

Fixed-term contract: 4 years.

TU Delft offers PhD-candidates a 4-year contract, with an official go/no go progress assessment after one year. Salary and benefits are in accordance with the Collective Labour Agreement for Dutch Universities, increasing from € 2325 per month in the first year to € 2972 in the fourth year. As a PhD candidate you will be enrolled in the TU Delft Graduate School. The TU Delft Graduate School provides an inspiring research environment with an excellent team of supervisors, academic staff and a mentor. The Doctoral Education Programme is aimed at developing your transferable, discipline-related and research skills.

The TU Delft offers a customisable compensation package, discounts on health insurance and sport memberships, and a monthly work costs contribution. Flexible work schedules can be arranged. For international applicants we offer the Coming to Delft Service and Partner Career Advice to assist you with your relocation.

Delft University of Technology

Delft University of Technology is built on strong foundations. As creators of the world-famous Dutch waterworks and pioneers in biotech, TU Delft is a top international university combining science, engineering and design. It delivers world class results in education, research and innovation. For generations, our engineers have proven to be entrepreneurial problem-solvers both in business and in a social context. TU Delft offers 16 Bachelor’s and 32 Master’s programmes to more than 23,000 students. Our scientific staff consists of 3,500 staff members and 2,800 PhD candidates. Together we imagine, invent and create solutions using technology to have a positive impact on a global scale.

Challenge. Change. Impact!

Faculty Electrical Engineering, Mathematics and Computer Science

The Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) brings together three disciplines - electrical engineering, mathematics and computer science. Combined, they reinforce each other and are the driving force behind the technology we use in our daily lives. Technology such as the electricity grid, which our faculty is helping to make future-proof. We are also working on a world in which humans and computers reinforce each other. We are mapping out disease processes using single cell data, and using mathematics to simulate gigantic ash plumes after a volcanic eruption. There is plenty of room here for ground-breaking research. We educate innovative engineers and have excellent labs and facilities that underline our strong international position. In total, more than 1,100 employees and 4,000 students work and study in this innovative environment.

Click here to go to the website of the Faculty of Electrical Engineering, Mathematics and Computer Science.