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.
5 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 the basics of tropical geometry. They can use tools from algebraic geometry, combinatorics and convex geometry for application in tropical geometry. Students will be able to familiarise themselves with a problem of current research in tropical geometry.
Students are able to give a specialised mathematical lecture independently. They can independently develop a mathematical problem from the field of Tropical Geometry, prepare it for a presentation, present it in an understandable way in the presentation and prepare a technically correct elaboration on the contents of the presentation. They will be able to independently fill any gaps, such as missing proofs/proof steps or missing illustrative examples.
With the seminar presentation and the preparation of the presentation, students develop both their ability to discuss and write mathematical texts. This prepares them further for the requirements of the Master's module, in particular the writing of the Master's thesis, the Master's seminar presentation including scientfic discussions and the defence of their Master's thesis.
In the seminar, students give a presentation on a mathematical problem of Tropical Geometry. The questions raised in the presentation are discussed with the participants of the seminar. Afterwards, the students prepare a paper on the presentation.
Topics for the seminar are:
Fields with valuations, polyhedral geometry, tropical polynomials and tropical hypersurfaces, Kapranov's Theorem
Possible supplementary topics are:
Milkhalikin's correspondence theorem, tropical moduli spaces, tropical intersection theory
Possible topics for the seminar are:
Fields with valuations, polyhedral geometry, tropical polynomials and tropical hypersurfaces, Kapranov's Theorem
Algebra, previous knowledge of algebraic geometry is helpful but not required.
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Module structure: 1 SL, 1 bPr 1
| Allocated examiner | Workload | LP2 |
|---|---|---|
|
Teaching staff of the course
Seminar Introduction in Tropical Geometry
(seminar)
Regular contributions to the scientific discussion in the seminar, for example in the form of comments and questions on the seminar presentations. |
see above |
see above
|
Correct and comprehensible presentation of a mathematical topic including essential steps of proof in a presentation, usually 90 minutes in length including a technical discussion.
Technically correct and comprehensible written elaboration of the presentation including essential proof steps, 5-10 pages in length.
| 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 |
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