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PhD position in mathematics or mathematical statistics, with focus on geometric deep learning

Department of Mathematics and Mathematical Statistics




  • Type of employment Temporary position
  • Extent 100%
  • Place Umeå

The Department of Mathematics and Mathematical Statistics is opening a PhD position in mathematics or mathematical statistics, focusing on geometric deep learning. The position covers four years of third-cycle studies, including participation in research and third-cycle courses. The last day to apply is August 26th 2024.

Project description and tasks 
Machine learning (‘artificial intelligence’) is having an immense impact on both society at large and research especially, and this impact is expected to increase. This boom is driven by so-called deep neural networks, a class of machine learning models proven incredibly powerful, versatile, and capable of solving many machine learning tasks. Mathematicians have taken huge steps towards theoretically understanding their empirical success, but many open questions remain.

A subfield within neural network theory is geometric deep learning. It concerns symmetries in the data or the learning task and constructing neural networks that react properly to them (equivariant networks). Examples of such symmetries are symmetries towards rotations of point clouds, translations of images or permutations of nodes in graphs. Combining the geometric/algebraic theory of (group) symmetries with the more analytical/statistical theory of machine learning allows for mathematically multifaceted research.

The project aims at deepening the mathematical theory of geometric deep learning. Exciting research questions include the development of new ways of constructing equivariant networks, describing the resulting models mathematically, and directly analyzing how symmetries affect the training of neural networks.

The project is affiliated with the AI/Math track within Wallenberg AI, Autonomous Systems and Software Program (WASP), and the PhD student will take part in the WASP graduate school.

The doctoral student will be admitted to study one of the two third-cycle programmes: Mathematics or Mathematical Statistics. To fulfil the general entry requirements, the applicant must have qualifications equivalent to a completed degree at second-cycle level or completed course requirements of at least 240 ECTS credits, including at least 60 ECTS credits at second-cycle level. 

To fulfil the specific entry requirements to be admitted for studies in either mathematics or mathematical statistics, the applicant is required to have completed at least 60 ECTS credits within mathematics or mathematical statistics, of which at least 15 ECTS credits shall have been acquired at second-cycle level. Applicants who have acquired largely equivalent skills in some other system, either within Sweden or abroad, are also eligible. 

Good programming skills (preferably Matlab or Python) and good written and spoken English knowledge are required. Documented knowledge and experience in machine learning, image analysis, probability theory, differential geometry, algebra, optimization, representation theory and functional analysis are merits. Note that you are not expected to have specialist knowledge in all of the above-listed fields. You will acquire knowledge as a part of your doctoral studies and be able to collaborate with others to complement your specific skill set.

You are expected to take an active role in this project and institutional work. You have a scientific mindset and are determined to continuously develop your skills and contribute to mathematical machine learning research. 

The assessment of applicants is based on their qualifications and ability to benefit from the doctoral study they will receive. 

About the employment 
The employment is a full-time paid position, for a fixed term of four years full-time or up to five years when teaching part-time. The position is intended to result in a doctoral degree.  The position is intended to result in a doctoral degree. The main task of doctoral students is to pursue their third-cycle studies, including active participation in research and third-cycle courses and activities and courses at the WASP graduate school. The duties may include teaching or other departmental work, although duties of this kind may not comprise more than 20 per cent of a full-time post. Salary is set according to the salary ladder for PhD positions at Umeå University. Employment commences in the winter of 2024/2025 or by agreement. 

You will become a part of the young and growing research group Mathematical Foundations of Artificial Intelligence at the Department of Mathematics and Mathematical Statistics. Most junior and senior researchers in this group are connected to WASP and research topics similar to those with which this project is concerned. This provides opportunities for exciting collaborations, both internally and externally. For more information, see https://www.umu.se/en/department-of-mathematics-and-mathematical-statistics/research/mathematical-foundations-of-artificial-intelligence/

The WASP graduate school is dedicated to providing the skills needed to analyze, develop, and contribute to the interdisciplinary area of artificial intelligence, autonomous systems and software. The graduate school actively supports forming a strong multi-disciplinary and international professional network between PhD students, researchers, and industry through an ambitious program that includes research visits, partner universities, and visiting lecturers. Read more: https://wasp-sweden.org/graduate-school/ 

Application should be made in our electronic recruitment system before August 26th 2024. Log in and apply using the button at the bottom of the page. The application must include the following documents written in English or Swedish: 

  • a personal letter with a brief description of your qualifications and research interests. Motivate why you are applying for the position and how your qualifications and merits are relevant.
  • a curriculum vitae.
  • authenticated copies of degree certificates, diplomas or equivalent, including documentation of completed academic courses, received grades, and possibly other certificates.
  • copies of relevant work such as a Master’s thesis or articles you have authored or co-authored. If the master’s thesis has not been completed before the application deadline, a summary of the master’s thesis project and current progress shall be included. The summary can be at most five pages, including figures and references.
  • contact information for at least two reference persons.
  • if available, GMAT, GRE, TOEFL or IELTS scores may be submitted.

Umeå University wants an equal environment where open dialogue between people with different perspectives lays the foundation for learning, creativity and development. The people working at the Department of Mathematics and Mathematical Statistics have diverse backgrounds and experiences, which we value. Work-life balance is essential for us: Employees are supported in caring for their mental and physical health, and we accommodate students taking parental leave during their studies – this is not uncommon. In this spirit, we encourage everyone to apply. 

Pursuant to Chapter 12 Section 2 of the Swedish Higher Education Ordinance (SFS 1993:100), the decision regarding the position cannot be appealed.

More information
Further information is provided by Professor Jun Yu (jun.yu@umu.se) or Assistant Professor Axel Flinth (axel.flinth@umu.se).

More information about the Department of Mathematics and Mathematical Statistics:

Wallenberg AI, Autonomous Systems and Software Program (WASP) is Sweden’s largest individual research program ever, a major national initiative for strategically motivated basic research, education, and faculty recruitment. The program addresses research on artificial intelligence and autonomous systems acting in collaboration with humans, adapting to their environment through sensors, information and knowledge, and forming intelligent systems-of-systems. The vision of WASP is excellent research and competence in artificial intelligence, autonomous systems and software for the benefit of Swedish society and industry. Read more: https://wasp-sweden.org/ 

Welcome with your application!

Information box


2025-01-01 or accoding to agreement



Application deadline


Registration number

AN 2.2.1-808-24


Axel Flinth, Associate Professor


Union representative







Umeå University wants to offer an equal environment where open dialogue between people with different backgrounds and perspectives lay the foundation for learning, creativity and development. We welcome people with different backgrounds and experiences to apply for the current employment. We kindly decline offers of recruitment and advertising help.