Post-doctor in numerical analysis - Hiring in process/Finished, not possible to apply

The position will be placed at the Division of Mathematics LTH and Numerical Analysis, Centre for Mathematical Sciences. The Centre currently has strong research environments in numerics for partial differential equations (PDEs) and machine learning, and will now start a new research group at the intersection of these areas. This group is expected to contribute to the grand challenges within mathematics for artificial intelligence (AI) and is funded by the Wallenberg AI, Autonomous Systems and Software Program. The successful candidate will thus be part of a highly stimulating and rewarding work environment, with the possibility of contributing to important modern-day problems. 

Work duties
The main duties involved in a post-doctoral position is to conduct research within the subject area. Teaching in the first, second and third cycles of studies may also be included, but up to no more than 20% of the working hours. The position shall include the opportunity for three weeks of training in higher education teaching and learning. The postdoctoral fellow is expected to interact with students and PhD students in the research group and to contribute to meetings and seminars.

Project description
The intended project aims to construct and analyse novel numerical methods for optimization problems arising in machine learning applications. Steepest descent-type methods, like the stochastic gradient method and the proximal point algorithm, are currently very popular for this task. However, by formulating the underlying problem as a gradient flow, one can observe that these methods are equivalent to stochastic perturbations of very basic time-stepping methods. Our intention is therefore to apply more advanced, modern time-stepping methods, which should lead to improved efficiency and robustness. The main task of this specific project is to perform rigorous error analyses for such time integration methods. In order to handle also large-scale (infinite-dimensional) situations, we will focus on analyses based on nonlinear semigroup theory and variational frameworks of monotone operators. Due to the presence of random sampling, also the theory of stochastic PDEs will be required.

Qualification requirements
Appointment to a post-doctoral position requires that the applicant has a PhD, or an international degree deemed equivalent to a PhD, within the subject of the position, completed no more than three years before the last date for applications. Under special circumstances, the doctoral degree can have been completed earlier.

Additional requirements:

• Very good oral and written proficiency in English.

Assessment criteria and other qualifications
This is a career development position primarily focused on research. The position is intended as an initial step in a career, and the assessment of the applicants will primarily be based on their research qualifications and potential as researchers. Particular emphasis will be placed on research skills within the subject.

For appointments to a post-doctoral position, the following shall form the assessment criteria:

• A very good ability to develop and conduct high quality research.
• Documented teaching skills.

Additional assessment criteria:

• Documented experience with functional analytic tools for error analysis in nonlinear semigroup frameworks, or similar settings.
• Documented experience with analysis of stochastic PDEs.

Consideration will also be given to good collaborative skills, drive and independence, and how the applicant’s experience and skills complement and strengthen ongoing research within the department, and how they stand to contribute to its future development.

Terms of employment
This is a full-time, fixed-term employment of a maximum of 2 years. The period of employment is determined in accordance with the agreement “Avtal om tidsbegränsad anställning som postdoktor” (“Agreement on fixed-term employment as a post-doctoral fellow”) between Lund University, SACO-S, OFR/S and SEKO, dated 4 September 2008.

Instructions on how to apply
Applications shall be written in English and must include a cover letter (1-2 pages) motivating why you want to conduct research in this field at Lund University, how the research matches your interests and scientific background, and how you would contribute to the research topic.

Applications must also include a CV, publication list, a copy of the applicant’s doctoral thesis, contact details of at least two references, copies of grade certificates, and any other documents that the applicant wishes to refer to (for example publications, letters of recommendation). Please compile all the documents except the thesis into a single PDF.