Umeå University, Faculty of Science and Technology

Umeå University is dedicated to providing creative environments for learning and work. We offer a wide variety of courses and programmes, world leading research, and excellent innovation and collaboration opportunities. More than 4 100 employees and 34 000 students have already chosen Umeå University. We welcome your application!

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 at Umeå University is opening a PhD position in mathematical statistics, focused on convex learning theory for deep neural netwroks. The position is for four years of doctoral studies which include both participation in research and postgraduate courses. Last day to apply is January 27, 2020.

The expansion of Artificial Intelligence (AI), in the broad sense, is one of the most exciting developments of the 21st century. This progress opens up many possibilities but also poses grand challenges. The centre Wallenberg AI, Autonomous Systems, and Software Program (WASP) is launching a program to develop the mathematical side of this area. The aim is to strengthen the competence of Sweden as a nation within the area of AI and we are taking part of this program through this specific project. The vision of WASP is excellent research and competence in artificial intelligence, autonomous systems and software for the benefit of Swedish industry. For more information about the research and other activities conducted within WASP please visit

Project description and tasks
Deep neural networks (DNNs) have revolutionized machine learning and artificial intelligence in the past few years. A mathematical theory of DNNs is rapidly developing to explain their success and guide the practitioners. Central to this theory is the generalization power of DNNs, which governs their performance on unseen data. Empirical risk minimization (ERM) is the prevalent theoretical framework for quantifying the generalization of DNNs, whereby the complexity of the hypothesis class of all DNNs with the same architecture is measured by its Rademacher complexity, VC dimension, or a similar notion of complexity.

Broadly speaking, the objective of this doctoral project is to advocate for a new theory of learning for neural networks that will address the fundamental shortcomings of the above-mentioned complexity measures, such as their often worst-case dependence on the hypothesis class and the data distribution. This project crucially aims to introduce a new notion of complexity for DNNs, and to potentially explore its applications in AI, including medical imaging, automated quality control, and self-driving cars, evaluated on both simulated and real data. The student is also expected to join the collaborations from our ongoing AI-related projects.

The project is part of the WASP Graduate School, see for more information. 

Admission requirements
Prerequisites include 240 ECTS credits (swe. Högskolepoäng) of higher education studies of which 60 ECTS credits should be on an advanced level (Master’s level).

In addition to these general requirements, the applicant is required to have completed at least 90 ECTS credits in mathematical statistics, of which at least 30 credits shall have been acquired at the advanced level (Master’s level). Applicants who in some other system either within Sweden or abroad have acquired largely equivalent skills are also eligible.

You have a degree of master of science in mathematical statistics, degree of master of science in applied mathematics, master of science in engineering or an equivalent degree in a related field.

Excellent programming skills (preferably MatLab, Python or R) are required.
Good knowledge of English language, both written and spoken, are key requirements. Documented knowledge and experience in signal processing and image analysis are merit.

You are expected to play an active role in this interdisciplinary cooperation and have a scientific and result-oriented approach for your work. You should therefore have a very good communication and collaboration ability. You are structured, flexible and solution-oriented.

The assessments of the applicants are based on their qualifications and their ability to benefit from the doctoral-level education they will receive.

Applicants with a degree not from a Swedish university are encouraged to provide results obtained from GMAT (and/or GRE) and TOEFL/IELTS tests if available.

About the employment
The position is intended to result in a doctoral degree and the main task of the PhD student is to pursue their doctoral studies which include both participation in research and postgraduate courses. The duties can include teaching and other departmental work (up to a maximum of 20%). The employment is limited to 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 position. The employment starts in the spring of 2020 or according to agreement. 

A complete application should contain the following documents:

  • a personal letter with a brief description of your qualifications and your research interests. Motivate why you are applying for the employment and describe how your qualifications and merits are relevant to the employment.
  • a curriculum vitae.
  • reinforced copies of diplomas or equivalent, including documentation of completed academic courses, grades obtained, and possibly other certificates.
  • copies of relevant work such as Master’s thesis or articles that you have authored or co-authored.
  • contact information for at least two reference persons.

The Department of Mathematics and Mathematical Statistics values ​​the qualities that an even gender distribution brings to the department, and therefore we particularly encourage female applicants.

You apply via our e-recruitment system Varbi. Log in and apply via the button at the bottom of the page. The deadline for applications is 2020-01-27.

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.

Further information
Further information is provided by Professor Jun Yu, +46 90 7865127, and Assistant Professor Armin Eftekhari, You can also contact the head of department Åke Brännström for additional questions at

Research at the Department of Mathematics and Mathematical Statistics is conducted within mathematics, mathematical statistics and computational science. Important cooperation partners include the Faculty of Science and Technology, the Faculty of Medicine, Umeå School of Business and Economics, Umeå School of Sport Sciences, the University Hospital, the Faculty of Forest Sciences at the Swedish University of Agricultural Sciences, as well as public authorities and industry. We provide education at all levels with a particular focus on civil engineering programs.

For more information see

We look forward to receiving your application!

Type of employment Temporary position longer than 6 months
Contract type Full time
First day of employment Spring of 2020 or according to agreement
Salary Monthly salary
Number of positions 1
Working hours 100%
City Umeå
County Västerbottens län
Country Sweden
Reference number AN 2.2.1-2081-19
  • Jun Yu, Professor,, +46 90 7865127
  • Armin Eftekhari, Assistant Professor,
  • Åke Brännström, Head of Department,
Union representative
  • SACO, +46(0)90 7865365
  • SEKO, +46(0)90 7865296
  • ST, +46(0)90 7865431
Published 20.Dec.2019
Last application date 27.Jan.2020 11:59 PM CET

Return to job vacancies