The Numerical Analysis and Applied Mathematics (NUMA) research unit is part of the Department of Computer Science of KU Leuven. NUMA develops and analyzes numerical algorithms and software for large-scale and complex problems in science and engineering. Our research comprises the whole range from fundamental research (including exploration of novel approximation strategies and numerical analysis) to software implementation and applications in other scientific and engineering domains. Algorithm design for specific applications is always done in collaboration with domain experts. Our research is clustered around the following themes: numerical linear algebra, scientific computing, uncertainty quantification, numerical simulation, optimization and control, numerical integration and nonlinear equations. The Department of Computer Science is located in the quiet outskirts of Leuven on the Arenberg III Campus, in a building adjacent to the Department of Mathematics. The campus is well-connected to the city of Leuven and the neighboring villages of Bertem, Heverlee, Kessel-lo, and Wilsele both by bike lanes and bus.
The PhD candidate will carry out fundamental scientific research on the ManiFactor project of professors J. Van der Veken (Department of Mathematics), R. Vandebril (Department of Computer Science) and N. Vannieuwenhoven (Department of Computer Science). Factor analysis is a data analysis technique that seeks to extract information from matrices and tensors through various low-rank decompositions. Such matrices and tensors can also be interpreted as multilinear functions. In this interpretation, factor analysis can be seen as a way to approximate functions by other functions that are much more efficient to evaluate. You will extend factor analysis to functions between manifolds, which are curved geometric objects that locally look like a Euclidean space. This generalization presents several interesting challenges primarily caused by the non-linearity of the domains. We will employ techniques from functional approximation, tensor decompositions, and Riemannian geometry to tackle some of these challenges. Research in this area will draw from an interesting blend of functional analysis, graph theory, numerical analysis, Riemannian optimization, and even some application domains. The research has both a theoretical as well as an applied component.
The majority of the applicant's time will be devoted to their research project and their formation as an independent researcher, which will include studying new mathematical techniques, reading papers, implementing software, computer experimentation, mathematical analysis, writing scientific articles, and presenting their results at international scientific conferences. In this process, they will be guided and mentored by the supervisors. The candidate will enroll in the PhD program and prepare a PhD dissertation on aforementioned research. Aside from the main research occupation, the candidates will be engaged by a limited teaching assignment (of small-scale practical sessions). This can include guiding Master's thesis students. In addition, the candidate will be encouraged to participate in extra-curricular activities and may be presented with opportunities to apply their expertise to support industry-driven consulting projects.
The project is a collaboration between the departments of mathematics and computer science. We encourage the candidate to foster and strengthen the interaction between these domains.
We are looking for a candidate with a Master's degree in applied or pure mathematics, broadly defined. At least one of the degrees must have been obtained with distinction. The ideal traits of a PhD student for this topic are creativity, independence, a methodological approach to problem solving, a scientific evidence-based mindset, resistance and tolerance of failures and set-backs, mathematical maturity, and a geometric intuition. The candidate is highly motivated to perform state-of-the-art research, wants to learn something new every day, and is not afraid of hands-on experimentation.
We expect that the training of the candidate included basic computer science (programming, data structures, and fundamental algorithms), numerical analysis (floating-point numbers, the effect of roundoff on a computer implementation of an algorithm), and mathematics (calculus, geometry, optimization). The candidate is encouraged to include relevant evidence of this in the application. Knowledge of the more advanced topics of differential geometry, functional analysis, and mathematical optimization are particularly strong assets, though expertise in all of these areas is not expected at the outset of the PhD.
The candidate is fluent in English, both written and verbally, as demonstrated for example by their Bachelor or Master's thesis, or other scientific output. Knowledge or a willingness to learn Dutch is an asset, but not a requirement.
KU Leuven is an inclusive employer. We especially encourage students from any underrepresented minorities to apply for this position.
We offer a fully funded PhD position at the Department of Computer Science in the Faculty of Engineering Science. This includes an appropriate research budget, a competitive salary, health insurance and other social benefits, and additional benefits provided by KU Leuven (which may include a leased bike, end-of-year vacation bonus, part-time work from home, sports facilities, reduction for cultural events, etc). The aim is that the research results in a PhD dissertation.
The Faculty of Engineering Science, through the Arenberg Doctoral School, offers academic and professional training courses. Some of these are mandatory, comprising essential skills such as a workshop on scientific integrity and training for teaching assistants. Others are elective and focus on diverse skills that can be useful in both an academic and professional setting, such as academic writing, effective presentations, and project management.
The candidate will be offered a shared office space in a stimulating, international environment at the Department of Computer Science. The office will be equipped with a docking station, computer screen, and portable computer. Additionally, the department offers a cafeteria, free coffee machine, showers and lockers, bike stalls, and potentially access to a nearby parking lot.
The Department of Mathematics and the Department of Computer Science are located in adjacent and connected buildings on the Arenberg III campus of KU Leuven in the quiet outskirts of Leuven.
Submit your application through KU Leuven's online application tool and be sure to include:
- a motivation letter,
- a detailed curriculum vitae,
- transcripts of university diplomas, and
- the contact information of two academic references.
Applications will be considered as soon as we receive them. The application may be closed earlier than the final application date in case a strong candidate has been found. Some flexibility in the starting date of the position is possible, but it must be before 2022.
For more information please contact either
Prof. dr. Nick Vannieuwenhoven, tel.: +32 16 37 39 54, mail: firstname.lastname@example.org
Prof. dr. Joeri Van der Veken, tel.: +32 16 32 70 17, mail: email@example.com
Prof. dr. Raf Vandebril, tel: +32 16 32 76 30, mail: firstname.lastname@example.org
You can apply for this job no later than October 29, 2021 via the online application tool
KU Leuven seeks to foster an environment where all talents can flourish, regardless of gender, age, cultural background, nationality or impairments. If you have any questions relating to accessibility or support, please contact us at diversiteit.HR@kuleuven.be.Mehr
|Titel||Manifactor: Factor Analysis for Maps into Manifolds|
|Job location||Oude Markt 13, 3000 Leuven|
|Veröffentlicht||August 24, 2021|
|Bewerbungsschluss||Oktober 29, 2021|
|Jobart||PhD/ Doktorand/in  |
|Fachbereiche||Algorithmen,   Datenstrukturen,   Programmiersprachen,   Analysis,   Angewandte Mathematik,   Geometrie und Topologie,   Wissenschaftliches Rechnen,   Computergestützte Mathematik  |