This PhD position is funded by the Marie Curie program of European Union through the innovative training network (ITN) POEMA on polynomial optimization – http://poema-network.eu. The PhD candidate will be hosted by the Real Algebra and Geometry (RAG) group in the Mathematics and Statistics Department of Konstanz University. The local RAG group has a strong expertise in real algebraic geometry and its applications to optimization, in particular moment problems.
– To commit adequate time and effort to the project to the research topics of the Marie Skłodowska-Curie Innovative Training Network POEMA
– To demonstrate a high level of commitment and personal initiative, also in identifying and resolving of problems
– To take the responsibility for the conduct and progress of the research
– To fulfil tasks required by the supervisors as part of the project, and to exchange regularly with the supervisors
– To write the thesis and, where appropriate to present seminars, to attend and present papers at conferences and publish sections of the work under the guidance of their supervisors
– Hold a Master’s degree in Mathematics, Computer Science, Engineering, or an equivalent diploma (at the date of recruitment).
– A solid background in at least one of either algebra, (real) algebraic geometry or optimization. Good programming skills are also a plus.
– Ability to communicate fluently in English (speaking and writing). Language skills in German are not required.
– Less than 4 years of a research career, and not have a doctoral degree.
– Not have resided in the country where the research training takes place for more than 12 months in the 3 years immediately prior to recruitment, not have carried out main activity in that country.
Polynomial optimization problems arising from applications frequently feature strong symmetries that one would like to take advantage of. One possible approach tries to detect the symmetries in SDP relaxations automatically, and then to reduce size using block decomposition. While one may find symmetries in this way even when they are hidden or poorly understood, such a technique can only be expected to work for small size problems. Another possibility is to analyse symmetries of SDP relaxations in advance. In principle, very large (even infinite) SDPs can often be reduced to small (in particular finite) SDPs in this way. But such an approach requires a considerable machinery of harmonic analysis tailored towards the specific problem, in particular for higher order relaxations. Instead we want to pursue a third approach, where the symmetry reduction is already done on the level of the original optimization problem before relaxation. The main difficulty then is to generalize Timofte’s degree principles to general group actions of reductive groups on affine varieties, and to relate them to the Procesi-Schwarz result
describing the orbit variety.
To apply for this position, please send your application before 30th June 2021 to POEMA Administrative Manager Linh Nguyen (email@example.com) including:
– A detailed CV including education, work experience, skills, dissertations, research interests,career objectives, and — if available at the date of submission — names and contact details of two referees, that can include the supervisor of the master thesis, willing to provide confidential letters of recommendation, a list of publications if any
– A motivation letter regarding the position as well as the POEMA network
– A transcript of the master studies’ grades (including the overall grade and an explanation ofthe grading system) and the master’s thesis if available;
– Any other supported documents (if any)