PhD candidate in Numerical Methods for Optimization on Riemannian Manifolds

PhD candidate in Numerical Methods for Optimization on Riemannian Manifolds

Job title: PhD candidate in Numerical Methods for Optimization on Riemannian Manifolds


Job description: This is NTNU

NTNU is a broad-based university with a technical-scientific profile and a focus in professional education. The university is located in three cities with headquarters in Trondheim.

At NTNU, 9,000 employees and 42,000 students work to create knowledge for a better world.

You will find more information about working at NTNU and the application process

About the position

The Department of Mathematical Sciences at NTNU is Norway’s largest university environment in mathematical sciences with 85 permanent staff members and about 100 doctoral students and postdoctoral fellows.

The department conducts research at an international high level within the disciplines of algebra, analysis, didactics of mathematics, differential equations, geometry/topology, numerical analysis, optimization, and statistics. Part of the research is also conducted in close cooperation with other fields of science and technology at NTNU, as well as in cooperation with industry and external research institutions.

We have a vacancy for a PhD fellowship in Numerical Analysis and Optimization at the Department of Mathematical Sciences at NTNU.

The goal is a completed doctoral education up to an obtained doctoral degree. The successful candidate will be offered a three-year position. The Department may offer a twelve-month extension with teaching duties. The workplace will be Trondheim.

With the emerging possibilities of measuring and processing data, many modern data appear in non-linear spaces like a Riemannian manifold. Still, the same data processing tasks, for example denoising, feature extraction, approximation or interpolation, appear. These can often be phrased as optimization tasks on the range of the data. They often turn out to be high-dimensional, non-smooth functions, that may at least locally be convex. These properties often allow for efficient optimization algorithms. In the Euclidean case and globally convex functions for example a primal-dual splitting like the Chambolle-Pock algorithm, a Douglas-Rachford splitting or ADMM. On Riemannian manifolds, some of these algorithms are available, for example the Douglas-Rachford splitting or quite recently the Chambolle-Pock algorithm based on a newly introduced Duality concept.

Duties of the position

The PhD project offers multiple research directions where one can develop and apply novel state-of-art computational methods, including

  • Generalising algorithms, to Riemannian manifolds and investigating their properties like convergence or a convergence rate,
  • Investigate properties of models, like total generalised variation (TGV) regularisation, for manifold-valued data,
  • Numerical investigation of the developed algorithms, for example to shape optimisation or manifold-valued data processing,
  • Investigating further applications towards automatic differentiation or machine learning for manifold-valued data and optimisation on manifolds.

Required selection criteria

The PhD-position’s main objective is to qualify for work in research positions. The qualification requirement is that you have completed a master’s degree or second degree (equivalent to 120 credits obtained at master`s level) with a strong academic background in numerical mathematics, numerical analysis, optimisation or equivalent education with a grade of B or better in terms of .

If you do not have letter grades from previous studies, you must have an equally good academic foundation. If you have a weaker grade background, you may be assessed if you can document that you are particularly suitable for a PhD education. Applicants who do not master a Scandinavian language must document a thorough knowledge of English (equivalent to a TOEFL score of 600 or more).

You must meet the requirements for admission to the .

MSc students who expect to complete their master’s degree studies by summer 2021 are also encouraged to apply. Employment will then be postponed until the master’s degree is finished.

The appointment is to be made in accordance with the regulations in force concerning and

Preferred selection criteria

  • Theoretical Knowledge in Differential Geometry, Convex Analysis and Data Processing, for example Image Processing
  • Experience in programming numerical methods is highly desirable, in particular knowledge and experience with programming languages, preferably Julia or Python.
  • Experience with Open Source packages and their development is a plus but not required
  • Good language skills: Written and oral in English and if possible Norwegian skills.

Personal characteristics

We are looking for someone who

  • is highly motivated for pursuing a PhD degree
  • has good communication skills
  • is dedicated to work both in an interdisciplinary team and independently
  • has the willingness to learn and to face interesting challenges

We offer

  • exciting and stimulating tasks in a strong international academic environment
  • an open and

with dedicated colleagues * favourable terms in the

The department has a strong focus on a good work environment for both permanent and temporary employees. As part of this effort, we offer both social and scientific activities for our PhD candidates.

Salary and conditions

PhD candidates are remunerated in code 1017, and are normally remunerated at gross from NOK 491 200 per annum before tax, depending on qualifications and seniority. From the salary, 2% is deducted as a contribution to the Norwegian Public Service Pension Fund.

The period of employment is 3 years with no teaching, but the department may offer a 4th year with teaching and other duties for approximately 25% of the entire 4-year period.

Appointment to a PhD position requires that you are admitted to the PhD programme in mathematics ( ) within three months of employment, and that you participate in an organized PhD programme during the employment period.

The engagement is to be made in accordance with the regulations in force concerning State Employees and Civil Servants, and the acts relating to Control of the Export of Strategic Goods, Services and Technology. Candidates who by assessment of the application and attachment are seen to conflict with the criteria in the latter law will be prohibited from recruitment to NTNU. After the appointment you must assume that there may be changes in the area of work.

It is a prerequisite you can be present at and accessible to the institution daily.

About the application

The application and supporting documentation to be used as the basis for the assessment must be in English.

Publications and other scientific work must follow the application. Please note that applications are only evaluated based on the information available on the application deadline. You should ensure that your application shows clearly how your skills and experience meet the criteria which are set out above.

The application must include:

  • CV, certificates and diplomas
  • transcripts and diplomas for bachelor’s and master’s degrees. If you have not completed the master’s degree, you must submit a confirmation that the master’s thesis has been submitted or started. For the case, that you just started your thesis, please provide a current transcript of your coursework.
  • Academic works – published or unpublished – that you would like to be considered in the assessment (up to 5 works)
  • Name and address of two to three referees

If all, or parts, of your education has been taken abroad, we also ask you to attach documentation of the scope and quality of your entire education, both bachelor’s and master’s education, in addition to other higher education. Description of the documentation required can be found . If you already have a statement from NOKUT, please attach this as well.

Joint works will be considered. If it is difficult to identify your contribution to joint works, you must attach a brief description of your participation.

In the evaluation of which candidate is best qualified, emphasis will be placed on education, experience and personal and interpersonal qualities. Motivation, ambitions, and potential will also count in the assessment of the candidates.

NTNU is committed to following evaluation criteria for research quality according to

General information

A good work environment is characterized by diversity. We encourage qualified candidates to apply, regardless of their gender, functional capacity or cultural background.

The city of Trondheim is a modern European city with a rich cultural scene. Trondheim is the innovation capital of Norway with a population of 200,000. The Norwegian welfare state, including healthcare, schools, kindergartens and overall equality, is probably the best of its kind in the world. Professional subsidized day-care for children is easily available. Furthermore, Trondheim offers great opportunities for education (including international schools) and possibilities to enjoy nature, culture and family life and has low crime rates and clean air quality.

As an employee at NTNU, you must at all times adhere to the changes that the development in the subject entails and the organizational changes that are adopted.

In accordance with The Public Information Act (Offentleglova), your name, age, position and municipality may be made public even if you have requested not to have your name entered on the list of applicants.

If you have any questions about the position, please contact Assoc. Prof. Ronny Bergmann, email: .

Please submit your application electronically via j with your CV, diplomas and certificates. Applications submitted elsewhere will not be considered. Diploma Supplement is required to attach for European Master Diplomas outside Norway. Chinese applicants are required to provide confirmation of Master Diploma from .

If you are invited for interview, you must include certified copies of transcripts and reference letters. Please refer to the application number 2021/58517 when applying.

Application deadline: 17.01.2022.

About Company:

NTNU – knowledge for a better world

NTNU – knowledge for a better world

The Norwegian University of Science and Technology (NTNU) creates knowledge for a better world and solutions that can change everyday life.

Department of Mathematical Sciences

We are Norway’s largest university environment in mathematical sciences. The Department has a particular responsibility for all basis education in mathematical sciences for engineering and natural science students at NTNU. We focus on long-term basic research and applied research at a high international level.
Our aim is to meet the society’s needs for mathematical and statistical expertise in business and public administration as well as in the research and education sector. is one of seven departments in the .

Expected salary:

Location: Trondheim, Trøndelag

Job date: Tue, 16 Nov 2021 23:11:13 GMT

Apply for the job now!

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