Vorträge in der Woche 06.11.2017 bis 12.11.2017
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Montag, 06.11.2017: "Das Monge-Kantorovich-Problem - alt und neu"
Dr. Martin Kell (Universität Tübingen)
Vorkolloquium um 16 Uhr (moderiert von Florian Johne): "Ein Crashkurs in Maßtheorie geodätischer Räume". Ich werde die grundlegende Strukturen, die für die Theorie des optimalen Transports benötigt werden, anschaulich einführen. <br>Zusammenfassung: Im Vortrag werde ich zeigen, wie man das Transportabbildungsproblem aus der Theorie des optimalen Transports auf zwei verschiedene Arten lösen kann. Während die erste Methode auf dem klassischen Theorem von Rademacher beruht, basiert die zweite Methode auf einer geometrisch sehr anschaulichen Idee, die keine Ableitungen benutzt und sich auf geodätische Maßräume verallgemeinern lässt.
| Uhrzeit: | 17:15 |
| Ort: | N14 |
| Gruppe: | Kolloquium |
| Einladender: | Die Dozentinnen und Dozenten des Fachbereichs Mathematik |
Mittwoch, 08.11.2017: Random matrices, free probability and the topological recursion
Felix Leid (Saarland Universität)
The theory of random matrices has many different applications in mathematics and physics, e.g. random matrices are related to combinatorics of maps, number theory or string theory. But they are also studied for their own sake, inparticular one studies their eigenvalue distribution and it turns out that often this quantity shows a deterministic behaviour as the size of the matrix grows. In order to study this limiting distribution a rewarding method is called loop equations. The latter were the starting point of the recent theory of topological recursion, more precisely the topological recursion solves the loop eqations and hence the question of the limiting behavior of nice random matrices. I will give a introductory talk on random matrices, in particular discussing the loop equations and highlight the connection to the topological recursion method.
| Uhrzeit: | 14:00 |
| Ort: | C-Bau, N 16 |
| Gruppe: | OS Geometry - Topological Recursion |
| Einladender: | Prof. H. Markwig |
Donnerstag, 09.11.2017: Asymptotically hyperboloidal graphical time-slices in the Schwarzschild space-time
Axel Fehrenbach
In this talk we will derive some specific examples of hypersurfaces in the Schwarzschild space-time which have an important role as examples in the the current research about the center of mass in general relativity. <br>These examples, so called "graphical time-slices", arise as graphs of smooth functions "over" the canonical time-slice in the Schwarzschild space-time. <br>After discussing the "general" case we will introduce the concept of asymptotical hyperbolicity and then consider the special case of (rotational symmetric, umbilic,) asymptotically hyperboloidal graphical time-slices. <br>Using these assumptions, the basic properties of graphical time-slices (and some thoughts about the Schwarzschild-anti-de Sitter space-time) we will derive and solve two ordinary differential equations for the function which defines these special graphical time-slices.
| Uhrzeit: | 14:15 |
| Ort: | S9 |
| Gruppe: | Oberseminar Geometrische Analysis, Differentialgeometrie und Relativitätstheorie |
| Einladender: | Cederbaum, Huisken |
Donnerstag, 09.11.2017: About (1+2)-dimensional „Schwarzschild“ and lower dimensional Relativity
Oliver Schön
Many concepts that are introduced for (1+3)-dimensional spacetimes have analogon in higher dimensions. In this presentation we will discuss weather the same thing can be said about lower dimensional Relativity. We motivate this analysis by working out some properties of the „Pseudo-Schwarzschild solution“, that is, the restriction of the Schwarzschild solution to the equatorial plane. This spacetime behaves quite similar as the higher dimensional Schwarzschild spacetimes, but not completely. We will argue why there cannot be an „exact“ Schwarzschild solution in (1+2) dimensions. <br><br>Finally, we talk about asymptotical flatness and the ADM-mass in two space dimensions and why those concepts operate differently in lower dimensions.
| Uhrzeit: | 15:15 |
| Ort: | S9 |
| Gruppe: | Oberseminar Geometrische Analysis, Differentialgeometrie und Relativitätstheorie |
| Einladender: | Cederbaum, Huisken |