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

Description of the workplace

The Centre for Mathematical Sciences consists of about 150 teachers, researchers and doctoral students. Staff at the department provides graduate training and research activities within many different areas of mathematics. You will belong to a newly established division whose research is concerned with algebra, analysis and dynamical systems.

Subject description

Possible research projects are described below and we intend to hire two doctoral students. The projects are listed in no particular order and without priority. Please write in the application which project(s) you are interested in.

1. Pluripotential theory: singularities and computations

This project is aimed at better understanding of so-called plurisubharmonic func-tions and their possible singularities. Plurisubharmonic functions appear in a natural way when studying holomorphic functions of several complex variables, and as solutions to a Dirichlet problem for the complex Monge-Ampère equation — an elliptic fully non-linear partial differential equation. In particular, we will study how different types of singularities for the boundary data affects the solutions to this Dirichlet problem. The idea is to attack this problem using a combination of mathematical theory and numerical analysis to do explicit computations. Depending on the candidate’s background and interests, the ratio of theory to computations can be adjusted. Contact person:  Frank Wikström (frank.wikstrom@math.lth.se)

2. Subalgebras in the polynomial algebra in one and several variable

The project is centered around descriptions of subalgebras of finite codimension in the polynomial ring using conditions. Such subalgebras are usually described by their generators, in some cases in form of a canonical basis. The project concerns the interplay between the two types of descriptions, and what properties of a subalgebra one can read off, or efficiently compute, given a certain description. Many of the foundational results found for descriptions by conditions in one variable hold for several variables as well. To clarify more exactly what can be said in the case of several variables and to explore applications and consequences of these results is one suitable theme, but there are also other possible paths to explore. Two possible areas of application are open key cryptography and (in the case of several variables) new methods for attacking Jacobi's conjecture. The work is of both theoretical and algorithmic nature: the results are often found from the interplay between the analysis of results of computations and theoretical understanding. Contact person:  Anna Torstensson (anna.torstensson@math.lth.se)

3. Slowly recurrent mappings in complex dynamics

This project focuses on problems in dynamical systems, mainly iteration of rational or transcendental functions in complex dynamics. In particular, one would like to understand the perturbation properties of so-called critically slowly recurrent mappings. For such maps, critical points are, under iteration, allowed to return to the critical set with certain limited speed. Probably this condition is generic (i.e., it is fulfilled for almost all maps). The project also has clear connections to ergodic theory, invariant measures and typical trajectories with respect to invariant measures, shrinking-target problems, etc. Contact person:  Magnus Aspenberg (magnus.aspenberg@math.lth.se)

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 can 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.

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.

Other assessment criteria:

• For the project Pluripotential theory: singularities and computation, knowledge in complex analysis and numerical methods for partial differential equations will be considered a merit.
• For the project Subalgebras in the polynomial algebra in one and several variables, knowledge in algebraic structures, commutative algebra and programming (including complexity theory) will be considered a merit.
• For the project Slowly recurrent mappings in complex dynamics, knowledge in complex analysis, ergodic theory and dynamical systems will be considered a merit.

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

We offer

Lund University is a public authority which means that employees get particular benefits, generous annual leave and an advantageous occupational pension scheme.
Read more on the University website about being a Lund University employee Work at Lund University. 

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 two doctoral students.

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.

Welcome to apply!