The PhD project will be centered around implicit shape representations, including those based on neural networks. For such representations, we are interested in connecting the number of stored coefficients to the possible geometric complexity of the resulting shapes, both in theory and in practice. For the analytical aspects, the main relevant mathematical tools are differential geometry, approximation theory and measure theory. On the numerical side, we would like to use this efficiency to recover the shapes themselves from indirect measurements, such as those in inverse problems appearing in medical imaging and non-destructive testing. For this, optimization and numerical methods for differential equations also come into play.

The successful candidate will be supervised by Dr. José A. Iglesias Martínez within the Mathematics of Imaging and AI group headed by prof. C. Brune at the Department of Applied Mathematics. Our group has geometric deep learning as one main focus and strong interdisciplinary links, in particular relating to shape analysis of cell imaging data.

• You have, or will shortly acquire, an MSc degree in mathematics;
• You have a strong background in analysis, geometry, or numerical analysis;
• You are motivated to sustain a theoretical focus while working in an application-driven area;
• You are proficient in English.

• As a PhD student at UT, you will be appointed to a full-time position for four years, with a qualifier in the first year, within a very stimulating and exciting scientific environment;
• An active research group, bridging applied and pure mathematics;
• Your salary and associated conditions are in accordance with the collective labour agreement for Dutch universities (CAO-NU);
• You will receive a gross monthly salary ranging from € 2.541,- (first year) to € 3.247,- (fourth year);
• There are excellent benefits including a holiday allowance of 8% of the gross annual salary, an end-of-year bonus of 8.3%, and a solid pension scheme;
• A family-friendly institution that offers parental leave (both paid and unpaid);
• You will have a training programme as part of the Twente Graduate School where you and your supervisors will determine a plan for a suitable education and supervision;
• We encourage a high degree of responsibility and independence, while collaborating with close colleagues, researchers and other staff.