Dieses Modul ist Teil einer langfristigen Gesamtlehrplanung für das Masterprogramm, die sicherstellt, dass in allen fünf Gebieten jedes Jahr jeweils mindestens Module im Umfang von 20 LP angeboten werden. Im Rahmen dieser Gesamtlehrplanung wird das Modul in unregelmäßigen Abständen angeboten.
10 Credit points
For information on the duration of the modul, refer to the courses of study in which the module is used.
Non-official translation of the module descriptions. Only the German version is legally binding.
Students master in advanced contents and methods of the theory of automorphic forms, in particular they can independently carry out complex proofs in this area requiring a high level of mathematical expertise.
Students are able to define central concepts of the theory (e.g. automorphic forms, bi-invariant differential operators) and apply them in context. They are able to combine methods from different areas, namely differential geometry, topology, algebra, number theory, complex analysis and functional analysis.
Accordingly, students recognise far-reaching connections to mathematical issues that have already been worked out. They can transfer and apply the knowledge and methods they have learnt so far to deeper mathematical problems. Students also expand their mathematical intuition as a result of a more intensive study.
Students are introduced to current research questions in the area of automorphic forms. They will be able to recognise and assess further development opportunities and research goals.
In combination with other in-depth modules, they will be able to write their own research papers, e.g. a master's thesis in the field of Automorphic Forms.
In the tutorials (in connection with lecture/seminar), students develop their ability to discuss mathematical topics and thus further prepare themselves for the requirements of the master's module, in particular for the technical discussion in the master's seminar presentation and the defence of their master's thesis.
The following advanced content of teaching from the field of Automorphic Forms is compulsory:
Automorphic forms on the hyperbolic plane, lift to the group SL(2,R), biinvariant differential operators, representations of SL(2,R).
In addition, the following content of teaching can be covered, for example:
p-adic numbers, adeles and ideles, Tate’s thesis, adelic group GL(2), representation-theoretic interpretation of Hecke operators, Eisenstein series, spectral theory.
This module prepares the content of a master's thesis.
Geometry/Topology, Algebraic Number Theory, Functional Analysis, Complex Analysis
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Module structure: 1 SL, 1 bPr 1
| Allocated examiner | Workload | LP2 |
|---|---|---|
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Teaching staff of the course
Tutorials Automorphic Forms
(exercise)
Regular completion of the exercises, each with a recognisable solution approach, as well as participation in the exercise groups for the module's lecture. As a rule, participation in the exercise group includes presenting solutions to exercises twice after being asked to do so as well as regular contributions to the scientific discussion in the exercise group, for example in the form of comments and questions on the proposed solutions presented. The organiser may replace some of the exercises with face-to-face exercises. |
see above |
see above
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(electronic) written examination in presence of usually 120 minutes, oral examination in presence or remote of usually 40 minutes, A remote electronic written examination is not permitted.
| Degree programme | Profile | Recommended start 3 | Duration | Mandatory option 4 |
|---|---|---|---|---|
| Mathematical Economics / Master of Science [FsB vom 28.02.2025] | Mathematics | 2. o. 3. | one semester | Compulsory optional subject |
| Mathematical Economics / Master of Science [FsB vom 28.02.2025] | Economics | 2. o. 3. | one semester | Compulsory optional subject |
| Mathematics / Master of Science [FsB vom 28.02.2025] | 2. o. 3. | one semester | Compulsory optional subject |
The system can perform an automatic check for completeness for this module.