Theses

A bachelor thesis in mathematics or in mathematical physics is not yet an independent scientific work. Instead, the main purpose is to understand a known result, formulate it properly and illustrate it with some, perhaps new examples.

At Chair X, we supervise bachelor theses on various topics. On the physical side we are interested in classical and quantum mechanics including in particular the transition between these two dominant theories in physics. On the mathematical side this results in topics with focus in differential geometry, functional analysis or algebra and their applications. If you are interested you should have visited at least some of the relevant lectures and participated in corresponding bachelor seminars.

Generally, a certain interest in the physical motivation of the questions and tasks in a bachelor thesis are not strictly needed but helpful to a large extend. Students of mathematical physics will have participated in typical lectures on theoretical mechanics and quantum mechanics anyway. For students of bachelor programs in mathematics this needs not to be the case. Nevertheless, also for them a bachelor thesis at Chair X is definitely possible.

The precise topic of a bachelor thesis is then determined individually depending on the interests and previously taken courses. A bachelor thesis can be written either in German or in English.

Master theses at Chair X are offered and supervised for the master programs in mathematics, mathematics international and mathematical physics.

In contrast to a bachelor thesis there is a certain scientific level expected, requiring more independence from the student but also allowing her to work in close proximity of current research. Although it is not required, a master thesis can often lead to new scientific results. On the one side, intensive supervision during the master thesis will be offered, on the other side active participation in the life at Chair X and in particular the Oberseminar Deformation Quantization is expected. Here all members present their own work and guests give talks about different topics.

As prerequisites a certain familiarity with methods from differential geometry will be necessary. But interest in techniques from algebra and/or functional analysis can also be useful. General interest in the motivation provided by physics is helpful, which requires some knowledge about the physical origins of the problems. In addition, the participation of at least one Research in Groups is presumed, from which possible topics for the thesis might emerge. A different Research in Groups in the area of differential geometry, functional analysis or algebra will be offered every semester.

The exact topic of the master thesis will be individually discussed according to the interests and prior knowledge of the student. A master thesis can be written either in German or in English.

A Ph.D. at our chair at first requires a significantly higher than average academic performance. Only then new scientific results can  be expected in the wide offer of the chair X. For a PhD it is necessary to get involved both in finding the relevant question and, of course, in the subsequent solution. In most cases, there is no precise problem but a suggestion or an idea. It is then the task of the doctoral candidate to formulate an exact and meaningful question, which then allows a solution. Methodically, a greater familiarity with techniques of differential geometry, functional analysis or algebra is expected as well as a certain interest in the physical motivations of the questions.