Vorträge in der Woche 28.10.2024 bis 03.11.2024
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Mittwoch, 30.10.2024: Towards Brill-Noether Theory for Spectral Curves
Clemens Nollau (Tübingen)
This talk is motivated by the classical study of curves via varieties of linear systems and the recent progress in understanding Brill-Noether Theory for curves with a fixed gonality. We give an approach to these problems for the class of spectral curves. To do this we define spectral curves via characteristic polynomials of Higgs bundles. We present results in two special cases: Canonical double covers and spectral curves over the projective line. In the end we give some outlook on ongoing work with Hitchin's spectral curves.
| Uhrzeit: | 10:15 - 11:15 |
| Ort: | C4H33 |
| Gruppe: | Oberseminar kombinatorische algebraische Geometrie |
| Einladender: | Daniele Agostini, Hannah Markwig |
Donnerstag, 31.10.2024: Geometric Inequalities and rigidity of static-type metrics
Prof. Dr. Allan Freitas (Federal University of Paraíba)
The search for solutions to Einstein's equations remains a core challenge in General Relativity, particularly in the study of static solutions. In the vacuum case, Boucher, Gibbons, and Horowitz established a three-dimensional inequality that sets an upper bound on the boundary area of a static manifold, with equality achieved when the manifold is a hemisphere. Employing specific integral identities, we extend this analysis to higher-dimensional static vacuum manifolds and explore similar results in sub-static spaces. In this latter context, we also derive some splitting-type results.
| Uhrzeit: | 14:00 |
| Ort: | Seminarraum S09 (C6H05) 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) |