Vorträge in der Woche 21.07.2025 bis 27.07.2025
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Montag, 21.07.2025: Asymptotic Stability of Solitons
Prof. Jonas Lührmann (Texas A&M)
Many wave phenomena in nature, from water waves to light pulses in optical fibers, can be described by nonlinear dispersive equations. Among their solutions, solitons are particularly remarkable: they are localized waves that retain their shape as they travel, behaving almost like particles despite being waves. In this talk, I will explain what solitons are and why they are important for understanding the long-time behavior of nonlinear dispersive equations. I will also discuss recent progress on the question of the asymptotic stability of solitons in lower-dimensional settings where the strong interactions between solitons and dispersive waves lead to especially rich dynamics.
| Uhrzeit: | 17:15 |
| Ort: | N14 |
| Gruppe: | Kolloquium |
| Einladender: | Teufel |
Donnerstag, 24.07.2025: Reduction Arguments via Asymptotic Correspondence of Initial Data Sets
Anna Sancassani (Universität Tübingen)
Motivated by the work of Cha and Khuri, who proposed a strategy to prove the positive mass theorem and other geometric inequalities in the asymptotically AdS-hyperbolic setting, we studied the effects of the correspondence between constant mean curvature (CMC) initial data sets and charges defined on pairs of initial data with corresponding backgrounds. I will introduce a definition of asymptotically corresponding initial data sets and prove a result concerning the associated geometric invariants, as formulated by Michel. These findings enable us to simplify the strategy proposed by Cha and Khuri and prove a positive mass theorem on asymptotically AdS-hyperbolic initial data, under certain additional conditions. If time permits, I will discuss potential methods to remove these supplementary conditions. This analysis simplifies the above-cited approach and shows how these reduction arguments can be generalized beyond the asymptotically hyperbolic case.
| Uhrzeit: | 14:00 |
| Ort: | Seminarraum C4H33 and virtual via zoom, for zoom link please contact Martina Neu |
| Gruppe: | Oberseminar Geometrische Analysis, Differentialgeometrie und Relativitätstheorie |
| Einladender: | Carla Cederbaum, Gerhard Huisken, zusammen mit Jan Metzger (Potsdam) |