Coupling for indefinite Sturm–Liouville and PT -symmetric operators

• Applicant: Professor Dr. Carsten Trunk
• Subject Area: Mathematics
• Term: from 2018 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 401706221

Prof. Dr. V. Derkach, is a full professor at the Vasyl Stus Donetsk National University in Vinnytsya (Ukraine). He is a world’s leading expert in extension theory and in the theory of indefinite interpolation problems. It is the main aim of the proposal to invite him to Ilmenau for teaching and conducting research as a Mercator Fellow. Prof. Dr. V. Derkach had to leave the city of Donetsk in 2014 with his research group due to the war in east Ukraine. Currently, working conditions in Vinnytsya are difficult and connections to colleagues from Europe or the US are not easy to establish. It is our aim to establish a fruitful and long lasting academic exchange between the research group of Prof. Dr. V. Derkach and the group around Prof. Dr. C. Trunk at the TU Ilmenau. Together with the Mercator fellow, it is planned to start an ambitious research programme including the following topics:• coupling method in spectral analysis of Sturm–Liouville operators with indefinite• coupling method in spectral theory of PT -symmetric operators and metamaterials, cloaking and invisibility,• generalized Stieltjes strings.Moreover, the Mercator fellow will deliver a selection of lectures. They are designed in such a way that (master) students will obtain an introduction to the research area of the Mercator Fellow, and PhD students at the TU Ilmenau will be guided towards new and challenging research activities.

• DFG Programme: Research Grants
• International Connection: Austria, Canada, Finland, Netherlands, Poland, Russia, Switzerland, USA
• Cooperation Partners: Professor Dr. Jussi Behrndt; Professor Dr. Paul Binding; Professor Dr. Petru Cojuhari; Professor Dr. Branko Curgus; Dr. Uwe Günther; Professor Dr. Seppo Hassi; Professor Dr. Sergii Kuzhel; Professor Dr. Naboko Sergei Nikolaevich; Dr. Petr Siegl; Professor Dr. H. S. V. de Snoo; Professor Dr. Gerald Teschl; Professor Dr.-Ing. Harald Woracek