Umeå University, Faculty of Science and Technology

Umeå University is one of Sweden’s largest higher education institutions with over 37,000 students and about 4,700 employees. The University offers a diversity of high-quality education and world-leading research in several fields. Notably, the groundbreaking discovery of the CRISPR-Cas9 gene-editing tool, which was awarded the Nobel Prize in Chemistry, was made here. At Umeå University, everything is close. Our cohesive campuses make it easy to meet, work together and exchange knowledge, which promotes a dynamic and open culture.

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The Department of Mathematics and Mathematical Statistics conducts research in computational mathematics, discrete mathematics, mathematical modelling and analysis, and mathematical statistics. Our teaching is conducted at all levels and includes mathematics, mathematical statistics and computational science. Among our partners are international research groups, academic institutions, public organizations and companies.

The Department of Mathematics and Mathematical Statistics is opening a PhD position in mathematical statistics, focusing on geometric deep learning. The position is for four years of doctoral studies, including participation in research and postgraduate courses. The last day to apply is September 19, 2022.

Project description and tasks
Machine learning, especially deep neural networks, has, during the early 21st century, had an immense impact on both research and society at large. This rapid development has made great progress possible and caused significant challenges. A subfield within machine learning is so-called geometric deep learning. This concept can mean many things, but at its core, the field is dealing with situations in which the in-data is of non-standard type. One can, for instance, consider 3D models, point clouds, or spherical images. To deal with such data poses special requirements on the network architectures.

One of the more interesting questions is the one of so-called equivariance. An essential property of the popular convolutional neural networks is translation equivariance; a translation of the in-data causes a translation of the out-data. With in-data of different types comes the need for equivariance with respect to other groups of transformations, both of discrete and continuous type. Examples of exciting research questions are how such networks can be constructed, how they can be trained, and their mathematical properties.

This project aims to develop new methods and new theories within geometric deep learning. This can, for instance, consist of the design of new network architectures, analysis of universality properties, explorations of a new class of transformations, and applications to simulated and real data. The PhD candidate is also expected to cooperate with our other ongoing AI-related projects.

The project is a part of 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, see for more information.

To be admitted for studies at the third-cycle level, the applicant is required to have completed a second-cycle level degree, or completed course requirements of at least 240 ECTS credits, of which at least 60 ECTS credits are at second-cycle level, or have an equivalent education from abroad, or equivalent qualifications. For third-cycle studies in mathematical statistics, the applicant must have completed at least 60 credits within the field of mathematical statistics, statistics and mathematics, of which at least 15 credits shall have been acquired at the second-cycle level.

Excellent skills in programming (preferably MatLab or Python) are required. Good knowledge in both written and spoken English is also a requirement. Documented knowledge and experience in signal processing, machine learning, image analysis,  differential geometry, and representation theory are merits.

You are expected to take on an active role within this project and institutional work. You have a scientific mindset, can work independently, and are structured, flexible and solution-oriented. Above all, you are determined to continuously develop your skills and contribute to mathematical machine learning research.

Applications will be assessed by the applicant’s qualification and ability to benefit from the graduate education they will receive.

About the position
The position is intended to result in a doctoral degree. The main task of the PhD candidate is to pursue their doctoral studies, including participation in research and doctoral courses, and to take part in the WASP graduate school. The duties may include teaching and other departmental work (up to a maximum of 20%). The employment is limited to the equivalent of four years of full-time (48 months) or up to five years for teaching part-time.  Salary is set in accordance with the established salary ladder for PhD positions. The employment starts in winter 2022/2023 or according to an agreement.

Applications should be made in our electronic recruitment system before September 19, 2022. Log in and apply through the button on the bottom of the page. The application can be written in English or Swedish and should include the following:

  • 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 for the position.
  • 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 thesis project and current progress shall be included. The summary can be at most five pages, including figures and references.
  • contact information to at least two reference persons.

Applicants are encouraged to supply results from GMAT (or GRE) and TOEFL tests, if available.

The Department of Mathematics and Mathematical Statistics values the qualities an even gender distribution brings to the department and particularly encourages female applicants.

The procedure for recruitment for the position is in accordance with the Higher Education Ordinance (chapter 12, 2§), and the decision regarding the position cannot be appealed.

More information
Further information is given by Professor Jun Yu (, Assistant professor Axel Flinth ( You can also contact the head of department Åke Brännström, for additional questions at

Information about the Department of mathematics and mathematical statistics at Umeå University can be found at

We look forward to receiving your application!

Type of employment Temporary position
Employment expires 2026-12-31
Contract type Full time
Number of positions 1
Full-time equivalent 100%
City Umeå
County Västerbottens län
Country Sweden
Reference number AN 2.2.1-1248-22
  • Jun Yu, professor,
  • Axel Flinth, assistant professor,
  • Åke Brännström, head of department,
Union representative
  • SACO, 090-7865365
  • SEKO, 090-7865296
  • ST, 090-7865431
Published 04.Aug.2022
Last application date 19.Sep.2022 11:59 PM CEST

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