PhD Scholarship in Differential Geometry

Technical University of Denmark



DTU Compute Section for Mathematics carries out fundamental mathematical research, with active groups in Algebra, Dynamical Systems, Functional Analysis, and Geometry. In addition to basic research, we also cooperate on projects with colleagues from industry and the applied sciences.

This PhD project is financed by the Independent Research Fund Denmark (Nature and Universe) project “Geometry and Lorentzian harmonic maps”. Lorentzian harmonic maps generalize solutions of the wave equation to the manifold setting. They constitute a fundamental class of non-linear partial differential equations. Many important problems in geometry can be represented by 1+1 dimensional wave maps, and these in turn can be studied by loop group techniques that have their origins in soliton theory. This project will focus on these geometries, for example, constant negative curve surfaces in 3-space and constant mean curvature surfaces in the 3-dimensional anti-de-Sitter space. 

Responsibilities and Tasks
Your primary task will be to conduct original research in the area described above with the goal to produce a PhD dissertation by the end of the 3-year program.

You will aim to answer difficult questions concerning global properties of the solutions to geometric problems, such as the formation of singularities, extendibility of solutions, and the construction of compact solutions.

You will learn to write articles reporting your original results, of a sufficiently high quality to appear in top scientific journals.

You will participate in international conferences in the relevant field, and, as part of the PhD program, you will have an external research stay abroad of 3-6 months.

It is a requirement of the program that all PhD students take advanced courses amounting to approximate 30 ECTS-points. As part of your salary, there is a requirement of performing additional tasks (about 3 months during the 3 years) in the area of teaching or other department work.

Candidates should have a two-year master's degree (120 ECTS points) or a similar degree with an academic level equivalent to a two-year master's degree. A good mathematical background including knowledge of differential geometry is essential, and preference will be given to candidates who can document knowledge of Lie groups, complex analysis and partial differential equations.

Approval and Enrolment
The scholarship for the PhD degree is subject to academic approval, and the candidate will be enrolled in one of the general degree programmes at DTU. For information about our enrolment requirements and the general planning of the PhD study programme, please see the DTU PhD Guide

We Offer
DTU is a leading technical university globally recognized for the excellence of its research, education, innovation and scientific advice. We offer a rewarding and challenging job in an international environment. We strive for academic excellence in an environment characterized by collegial respect and academic freedom tempered by responsibility.

Salary and Appointment Terms
The appointment will be based on the collective agreement with the Danish Confederation of Professional Associations. The allowance will be agreed upon with the relevant union. The period of employment is 3 years. Starting data is 1 Sep 2019 or according to mutual agreement.

You can read more about career paths at DTU here

Further Information
Further information concerning the project can be obtained from David Brander, in the Section for Mathematics at DTU Compute.

Information concerning the application is available at the DTU Compute PhD homepage or by contacting PhD coordinator Lene Matthisson +45 4525 3377. 

You can read more about the Department at

Please submit your online application no later than 30 June 2019 (23:59 local time). Applications must be submitted as one PDF file containing all materials to be given consideration. To apply, please open the link "Apply online", fill out the online application form, and attach all your materials in English in one PDF file. The file must include: 

  • A letter motivating the application (cover letter)
  • Curriculum vitae
  • Grade transcripts and BSc/MSc diploma
  • Excel sheet with translation of grades to the Danish grading system (see guidelines and Excel spreadsheet here)
Candidates may apply prior to obtaining their master's degree but cannot begin before having received it.

Applications and enclosures received after the deadline will not be considered.

All interested candidates irrespective of age, gender, race, disability, religion or ethnic background are encouraged to apply.

DTU Compute is an internationally unique academic environment spanning the science disciplines mathematics, statistics and computer science. We also cover informatics and communication technologies (ICT) in their broadest sense. Finally, we play a major role in addressing the societal challenges of the digital society where ICT is a part of every industry, service, and human endeavour.

DTU is a technical university providing internationally leading research, education, innovation and scientific advice. Our staff of 6,000 advance science and technology to create innovative solutions that meet the demands of society, and our 11,200 students are being educated to address the technological challenges of the future. DTU is an independent university collaborating globally with business, industry, government and public agencies.

In your application, please refer to


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