Vorträge in der Woche 11.07.2022 bis 17.07.2022
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Donnerstag, 14.07.2022: Fano-Faserungen auf torischen Hyperflächen
Prof. Dr. Victor Batyrev (Universität Tübingen)
Nicht-degenerierte torische Hyperflächen X mit dem Newton-Polytop P besitzen negative Kodaira-Dimension genau dann, wenn das Fine-Innere F(P) des Polytops P leer ist. Im letzten Fall ist X zu einer Fano-Faserung birational isomorph. Im Vortrag betrachten wir eine kombinatorische Konstruktion für diese Faserung.
| Uhrzeit: | 14:00 |
| Ort: | Die Veranstaltung findet online statt. Den Zoom-Link erhalten Sie per E-Mail von Frau Martina Neu. |
| Gruppe: | Oberseminar Algebraische Geometrie |
| Einladender: | Batyrev, Hausen, Th. Markwig |
Donnerstag, 14.07.2022: The magnetic spectral triple: applications and open questions
Dr. Giuseppe De Nittis (Chile)
Since the early works by Bellissard, non-commutative geometry (NCG) has proved to be an excellent tool for the analysis of the quantum Hall effect (QHE), and more in general for the study of the topological phases of matter. The central object of the Bellissard's NCG for the QHE is a spectral triple designed to deal with tight-binding operators. In this talk we will present a new spectral triple suitable to treat continuous magnetic operators. We will show how the QHE in the continuous can be described inside this new NCG. Certain possible new applications, along with some related open questions, will be also presented.
| Uhrzeit: | 16:00 |
| Ort: | C3N16 |
| Gruppe: | Oberseminar Mathematical Physics |
| Einladender: | Capel, Keppeler, Lemm, Pickl, Teufel, Tumulka |
Freitag, 15.07.2022: Isoperimetric and Sobolev inequalities in Riemannian manifolds
Prof. Dr. Simon Brendle (Columbia University)
I will present a proof, using the ABP technique, of the Sobolev inequality in a manifold of nonnegative Ricci curvature. This method also gives a Michael-Simon-Sobolev inequality for submanifolds in ambient spaces with nonnegative sectional curvature.
| Uhrzeit: | 14:45 |
| Ort: | Hörsaalzentrum 7 E 02 |
| Gruppe: | Geometric Analysis Minisymposium |
| Einladender: | Huisken |
Freitag, 15.07.2022: On a generalized Geroch conjecture
Dr. Florian Johne (Columbia University)
Closed manifolds with topology N = M x S^1 do not admit metrics of positive Ricci curvature by the theorem of Bonnet-Myers, while the the resolution of the Geroch conjecture implies that the torus T^n does not admit a metric of positive scalar curvature. In this talk we explain a non-existence result for metrics of positive m-intermediate curvature (a notion of curvature reducing to Ricci curvature for m = 1, and scalar curvature for m = n-1) on closed manifolds with topology N^n = M^{n-m} x T^m for n <= 7. Our proof uses minimization of weighted areas, the associated stability inequality, and delicate estimates on the second fundamental form. This is joint work with Simon Brendle and Sven Hirsch.
| Uhrzeit: | 15:50 |
| Ort: | Hörsaalzentrum 7 E 02 |
| Gruppe: | Geometric Analysis Minisymposium |
| Einladender: | Huisken |