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.

1. Spectral theory for Schrödinger operators and nonlinear waves

An embedded eigenvalue of an operator is an eigenvalue which also belongs to its continuous spectrum. Such eigenvalues occur for example in quantum mechanics and in the study of stability of nonlinear waves. The aim of the project is to study embedded eigenvalues e.g. for time-independent Schrödinger operators, using spatial dynamical techniques, in which the eigenvalue equation is rewritten as a system of ordinary differential equations in a suitable function space. The solutions of this system are then studied using functional analysis methods and the theory of differential equations. Particular emphasis is establishing perturbation theory results, where we study the fate of an embedded eigenvalue when a small perturbation is added to the original operator. Associated with the project is also answering pertinent stability questions for nonlinear waves described by partial differential equations.

Contact person: Sara Maad Sasane (sara.maad_sasane@math.lth.se)

2. Statistical and fractal properties of dynamical systems related to recurrence

In this project, we will study statistical properties of chaotic  dynamical systems, in particular questions relating to recurrence and hitting. Some possible directions of research are dynamical  Borel–Cantelli lemmata, quantitative recurrence, and fractal sets  related to these kind of questions. The aims of the project are both  to find new kinds of theorems, as well as to extend previously known  ones to new classes of dynamical systems.

Contact person: Tomas Persson (tomas.persson@math.lth.se)

3. Compressed sensing and hyperspectral image reconstruction from aperture coded acquisition of spectroscopic data.

The aim of this PhD project is to develop and analyse mathematical models for an optical acquisition technique in hyperspectral imaging known as coded aperture snapshot spectral imaging (CASSI), and to devise fast and reliable algorithms for reconstruction of the original optical signal from one or more CASSI-measurements.

Raman spectroscopy, which can be used for detection of hazardous substances at standoff distance, will be of particular interest. CASSI allows for rapid acquisition of spectroscopic data, which is important in many time-critical applications. The cost of speed is that the spatial and spectral components of the signal get mixed up, so reconstruction becomes a highly ill-conditioned inverse problem. Inherent sparsity in the underlying signal ensures that reconstruction is possible, but existing algorithms are slow and constitute a bottleneck in the entire process; faster and more reliable methods are needed. To achieve this goal, tools from functional analysis, modern convex optimization and elements of scientific computing will be used. Modern machine learning methods may play a role later in the project.

Contact person: Niels Christian Overgaard (niels_christian.overgaard@math.lth.se)

Admission requirements

A person meets the general admission requirements for third-cycle courses and study programmes if the applicant: 

• 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 the applicant 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 Master’s 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

1. Knowledge and skills relevant to the thesis project and the subject of study.
2. An assessment of ability to work independently and to formulate and tackle research problems.
3. Written and oral communication skills.
4. 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 assessment criteria

For the project Spectral theory for Schrödinger operators and nonlinear waves, knowledge in functional analysis and the theory of differential equations will be considered a merit.

For the project Statistical and fractal properties of dynamical systems related to recurrence, knowledge in dynamical systems theory will be considered a merit.

For the project Compressed sensing and hyperspectral image reconstruction from aperture coded acquisition of spectroscopic data, skills in computer programming will be 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 up to 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 question as the first step of the application process.