Non-smooth spaces naturally arise in various branches of mathematics and its applications, for instance as limits of smooth Riemannian manifolds, through singularity formation in geometric flows or as discrete structure in data.
A natural framework for non-smooth spaces are metric measure spaces, i.e. spaces equipped only with the structure of a metric and a reference measure. In this seminar we will study analytic and geometric properties of such spaces and in particular how to develop a notion of curvature (lower bounds) for these objects using the theory of optimal transport.
Metric measure spaces with curvature bounds provide a robust framework that allows for the development of far reaching analytic and geometric results akin to classical results for smooth manifolds such a diameter and volume growth estimates or isoperimetric inequalities. The investigation of this class of spaces has been a highly active research field in the last decade and continues to spawn fascinating new developments.
We will work on familiarising ourselves with the foundations of the theory, developing central results and highlighting some recent developments according to the preferences of the participants.
Possible topics include:
Preliminary meeting: Tuesday October 17 16:00
If you are interested in the seminar but not able to attend the meeting, please contact me by email.
The seminar will take place starting from December 2023. The precise schedule will be arranged according to the participants.
Background in measure theory and functional analysis is desired. Depending on the topic, knowledge in Riemannian geometry and or PDEs is helpful.
Rhythmus | Tag | Uhrzeit | Format / Ort | Zeitraum |
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Modul | Veranstaltung | Leistungen | |
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24-M-P1 Profilierung 1 | Profilierungsseminar | Studienleistung
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Studieninformation |
24-M-P1a Profilierung 1 Teil A | Profilierungsseminar | Studienleistung
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Studieninformation |
24-M-P1b Profilierung 1 Teil B | Profilierungsseminar | Studienleistung
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Studieninformation |
24-M-P2 Profilierung 2 | Profilierungsseminar | Studienleistung
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Studieninformation |
24-M-PWM Profilierung Wirtschaftsmathematik | Profilierungsseminar | Studienleistung
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Studieninformation |
Die verbindlichen Modulbeschreibungen enthalten weitere Informationen, auch zu den "Leistungen" und ihren Anforderungen. Sind mehrere "Leistungsformen" möglich, entscheiden die jeweiligen Lehrenden darüber.
Studiengang/-angebot | Gültigkeit | Variante | Untergliederung | Status | Sem. | LP | |
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Mathematik / Promotion | Subject-specific qualification | 1 |