This projects seeks to investigate special instances of (mixed) integer programs ((M)IPs) with the intention of rendering them polynomial time solvable or establishing their hardness. Although traditionally known to be NP-hard, certain structured forms of (M)IPs exhibit properties that allow for efficiently finding solutions. Examples include block-structured (M)IPs, (M)IPs with a limited number of rows or columns, and (M)IPs whose constraint matrix is totally unimodular. Despite many recent advances in this field, numerous unresolved questions persist within this domain, and this project aims to solve some of them.

By solving such (M)IPs more efficiently, we further aim to design new algorithms for a broad spectrum of problems from combinatorial optimization. The relevance of (M)IPs spans across various applications where optimization plays a pivotal role. From supply chain management to resource allocation, encompassing fair division and voting rules among others, the ability to efficiently solve (M)IPs holds significant implications for operational efficiency, cost reduction, and decision-making processes. Moreover, recent developments in the field of machine learning have established a strong connection between these structures and neural networks, which we seek to fortify by developing robust algorithms tailored to these specific MIP classes.

The successful candidate for this Ph.D. position will work under the supervision of Alexandra Lassota in the group Combinatorial Optimization (https://www.tue.nl/en/research/research-groups/mathematics/statistics-probability-and-operations-research/combinatorial-optimization-1) of the department of Mathematics and Computer Science of TU/e. Your responsibilities include to perform scientific research on the topic of the above-mentioned project and to publish your results at international conferences and in international journals. For a small percentage of your time, you will be asked to assist with educational tasks (course support and supervision of students).

• You have a bachelor and master degree in Mathematics or an equivalent field.
• You are creative, ambitious, self-motivated, and have good communication skills.
• You have a good command of the English language (knowledge of Dutch is not required).

A meaningful job in a dynamic and ambitious university, in an interdisciplinary setting and within an international network. You will work on a beautiful, green campus within walking distance of the central train station. In addition, we offer you:

• Full-time employment for four years, with an intermediate evaluation (go/no-go) after nine months. You will spend 10% of your employment on teaching tasks.
• Salary and benefits (such as a pension scheme, paid pregnancy and maternity leave, partially paid parental leave) in accordance with the Collective Labour Agreement for Dutch .
• A year-end bonus of 8.3% and annual vacation pay of 8%.
• High-quality training programs and other support to grow into a self-aware, autonomous scientific researcher. At TU/e we challenge you to take charge of your own learning process.
• An excellent technical infrastructure, on-campus children's day care and sports facilities.
• An allowance for commuting, working from home and internet costs.
• A Staff Immigration Team for international candidates.