Coupling for indefinite Sturm–Liouville and PT -symmetric operators

V. Derkach博士教授是位于文尼茨亚（乌克兰）的顿涅茨克国立大学的正教授。他在可拓理论和不定插值问题理论方面是世界领先的专家。该提案的主要目的是邀请他作为墨卡托研究员到伊尔梅瑙进行教学和研究。2014年，由于乌克兰东部的战争，德卡奇教授不得不带着他的研究小组离开顿涅茨克市。目前，Vinnytsya的工作条件很艰苦，与来自欧洲或美国的同事建立联系也不容易。我们的目标是在伊尔梅瑙工业大学V. Derkach教授的研究小组和C. Trunk教授周围的小组之间建立一个富有成果和持久的学术交流。与墨卡托研究员一起，计划开始一个雄心的研究计划，包括以下主题：•不确定Sturm-Liouville算子光谱分析中的耦合方法•PT对称算子和超材料、隐形和不可见的光谱理论中的耦合方法；•广义Stieltjes弦。此外，墨卡托奖学金获得者将提供一系列精选讲座。他们的设计方式是（硕士）学生将获得对墨卡托研究员研究领域的介绍，而伊尔梅瑙工业大学的博士生将被引导到新的和具有挑战性的研究活动。

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.