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Resonances of Schottky Surfaces

(Prof. Dr. Anke Pohl)

Resonances of differential operators on spaces of all kinds play an important role in diverse areas of mathematics and have many applications, e.g. in physics. Among curved spaces, the Schottky surfaces are recommended as the first object of study. It has recently been observed that the resonance sets for the Laplace operator exhibit certain structures (see figure below). In this project, we study properties of the resonance sets of Schottky surfaces.

Basic knowledge of calculus as well as linear algebra is recommended, and basic knowledge of numerics would be beneficial. The duration of the research within the working group should be at least four weeks. In addition, a written paper and a final presentation in the seminar are expected.