PhD student/-s in mathematics - Hiring in process/Finished, not possible to apply

Work duties
The Ph. D. program in mathematics can contain pure as well as applied mathematics in various combinations. A list of possible research areas is included at the end of this document. The final choice of project and thesis advisor will be made jointly by the candidate and the department.

Possible research areas
In this call, we have one specific project within WASP (Wallenberg Autonomous Systems and Software Program) as well as more general projects within some of the department's areas of expertise.  Areas and persons are listed alphabetically with no particular priority. We are planning to fill two or three positions. Contacts within each areas in parentheses.

Optimization methods for matrix factorization, dimensionality reduction and deep networks. 
In recent years there has been a dramatic increase in performance of recognition, classification and segmentation systems due to deep learning approaches, in particular convolutional nets. State-of-the-art methods are now able to achieve recognition with the same accuracy as humans on thousands of object categories. Still there is very little theoretical understanding of the reason for this improvement. Furthermore, training with these models requires solving very large scale non-convex optimization problems and it is unclear under what conditions these can be reliably solved. In this project we will study mathematical optimization methods for learning and dimensionality reduction approaches related to matrix factorization. We will develop effective and reliable algorithms that scale well beyond today’s standard and apply these to computer vision applications. Additionally, we aim to characterize what different learning architectures can achieve and provide theoretical limits on their performance (Contact: Carl Olsson, WASP)

Dynamical systems. 
Possible specializations: Complex dynamics, i.e. iteration of meromorphic functions, dimension theory, e.g. Hausdorff and Fourier dimensions of dynamically defined sets. Statistical properties and ergodic theory for dynamical systems (Contact: Magnus Aspenberg, Tomas Persson, Jörg Schmeling).

Partial differential equations and modelling.
Possible specializations: Embedded eigenvalues for partial differential equations from mathematical physics. Stochastic modelling of traffic flow using artificial intelligence techniques. Domain decomposition method for numerical solutions of partial differential equations (Contact: Eskil Hansen, Sara Maad Sasane, Alexandros Sopasakis)

Spectral theory and complex analysis.
Possible specializations: Spectral theory for periodic and almost-periodic operators. Interpolation and extremal problems in one and several complex variables (Contact: Jacob Stordal Christensen, Frank Wikström).

Please note in the application which area(s) you are interested in!

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 will also teaching and other departmental duties (no more than 20%).

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 wich 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 Master of Science programs in Engineering Mathematics or Engineering Physics or 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.

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 §§.

 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.).