Doctoral students in mathematics - Hiring in process/Finished, not possible to apply

Work duties
The main duties of doctoral students are to devote themselves to their research studies, which includes participating in research projects and third cycle courses. The work duties may also include teaching and other departmental duties (no more than 20%). The PhD program in mathematics can contain pure as well as applied mathematics in various combinations. 

Possible research Projects
We are looking for a doctoral student to each of the following projects. The projects are listed in no particular order and without priority. Please note in the application which project(s) you are interested in.

Monotonicity for magnetic Schrödinger operators
In this project we use tools from spectral theory, partial differential equations, Hilbert space theory, semi-classical analysis and asymptotic analysis to study problems on monotonocity for parameter-dependent eigenvalues of the magnetic Schrödinger operator in domains in the plane or the space.

We are in particular interested in the monotonicity of the smallest eigenvalue, both with respect to the strength of the magnetic field in domains with symmetry, and with respect to the opening angle of domains with corners.

This type of monotonicity questions has proven to be important to understand phase transitions in the theory of superconductivity. It has been studied intensively during the last decades, and our goal is to answer them in some particular cases not covered by the general theory.

Contact: Mikael Persson Sundqvist

Algorithms for analysis and synthesis of images and video
This project concerns machine learning and computer vision. The focus is on developing new methods and machine learning algorithms for analysis and synthesis of images and video.

The goal is to develop new methods for finding properties and features in observations. For example, estimating positions of objects in images, computing and estimating a 3D-model and texture of an object based on images alone, generating synthetic data or using multiple views with known or partially known sensor properties.

You will use the latest state-of-the-art-research in machine learning, for example auto encoders, convolutional neural networks, optimisation, adversarial networks, disentanglement, transfer learning and image generation and synthesis. These methods will be combined with methods from computer vision such as 3D-reconstruction, calibration and mapping.

Contact: Mikael Nilsson

Applied mathematics with nonlinear partial differential equations
In this project, we are interested in real nonlinear processes in industry and life science that for some reason need to be modelled, simulated and controlled, and where investigations made in other sciences can be improved by using advanced mathematics and numerical analysis.

Applications are two- or three-phase flows in separation processes such as sedimentation, flotation, centrifugation, chromatography and slow sand filtering. Other applications are traffic and pedestrian flows. The conservation laws of mass and momentum of mixtures lead to models formulated as nonlinear convection-diffusion-reaction and coupled-flow equations.

The research comprises mathematical and numerical analysis, control and inverse problems of nonlinear partial differential equations of hyperbolic-parabolic type.

Contact: Stefan Diehl

Admission requirements
A person meets the general admission requirements for third-cycle courses and study programmes if he or she

• has been awarded a second-cycle qualification, or
• has satisfied the requirements for courses comprising at least 240 credits of which at least 60 credits were awarded in the second cycle, or
• has acquired substantially equivalent knowledge in some other way in Sweden or abroad.

A person meets the specific admission requirements for third cycle studies in mathematics if he or she has

• at least 90 credits of relevance to the subject area, of which at least 60 credits from the second cycle and a specialised project of at least 30 second-cycle credits in the field, or
• a second second-cycle degree in a relevant subject.

In practice this means that the student should have achieved a level of knowledge in mathematics that corresponds to that of a Master of Science programs in Engineering Mathematics or Engineering Physics alternatively a Masters degree in mathematics or applied mathematics.

Additional requirements:

• Very good oral and written proficiency in English

Assessment criteria
Selection for third-cycle studies is based on the student’s potential to profit from such studies. The assessment of potential is made primarily on the basis of academic results from the first and second cycle. Special attention is paid to the following

• Knowledge and skills relevant to the thesis project and the subject of study.
• An assessment of ability to work independently and to formulate and tackle research problems.
• Written and oral communication skills.
• Other experience relevant to the third-cycle studies, e.g. professional experience.

Consideration will also be given to good collaborative skills, drive and independence, and how the applicant, through his or her experience and skills, is deemed to have the abilities necessary for successfully completing the third cycle programme.

Other assessement criteria

• For the projects Algorithms for analysis and synthesis of images and video and Applied mathematics with nonlinear partial differential equations, experience with computer programming, especially in relevant areas, is considered a merit. 

Terms of employment
Only those admitted to third cycle studies may be appointed to a doctoral studentship. Third cycle studies at LTH consist of full-time studies for 4 years. A doctoral studentship is a fixed-term employment of a maximum of 5 years (including 20% departmental duties). Doctoral studentships are regulated in the Higher Education Ordinance (1993:100), chapter 5, 1-7 §§.

We intend to hire three doctoral students. 

Instructions on how to apply
Applications shall be written in English and include a cover letter stating the reasons why you are interested in the position and in what way the research project corresponds to your interests and educational background. The application must also contain a CV, degree certificate or equivalent, and other documents you wish to be considered (grade transcripts, contact information for your references, letters of recommendation, etc.).

You are also required to answer the job specific questions as the first step of the application process.