Vorträge in der Woche 04.02.2019 bis 10.02.2019
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Montag, 04.02.2019: The moduli space of matroids
Prof. Dr. Oliver Lorscheid (IMPA, Rio de Janeiro/MPI Bonn)
Vorkolloquium um 16 Uhr moderiert von Christoph Goldner. Matroids are combinatorial gadgets that reflect properties of linear algebra in situations where this latter theory is not available. This analogy prescribes that the moduli space of matroids should be a Grassmannian over a suitable base object, which cannot be a field or a ring; in consequence usual algebraic geometry does not provide a suitable framework. In joint work with Matt Baker, we have used algebraic geometry over the so-called field with one element to construct such moduli spaces. As an application, we streamline various results of matroid theory and find simplified proofs of classical theorems, such as the fact that a matroid is regular if and only if it is binary and orientable. We will dedicate the first part of this talk to an exposition of matroids. Then we will briefly outline how to construct the moduli space of matroids. In a last part, we will explain with some care why this theory is useful to simplify classical results in matroid theory. Except for the expository part on the construction of the moduli spaces, we do not assume any specialized knowledge. In the precolloquium, we will give an extended introduction to matroids.
| Uhrzeit: | 17:15 - 18:15 |
| Ort: | N 14 |
| Gruppe: | Kolloquium |
| Einladender: | Hannah Markwig |
Dienstag, 05.02.2019: KdV-Gleichung, Riemannsche Flächen und ihre Deformationen, Teil IV
Jonas Ziefle (Universität Tübingen)
Entsprechend der adiabatischen Änderung von Erhaltungsgrößen bei klassischen integrablen Systemen kann der isospektrale Ansatz für die KdV-Gleichung "langsam" moduliert werden (nichtlinearer WKB-Ansatz). Dabei soll die Quasiperiodizität von Lösungen erhalten bleiben. Dies führt auf dispersionslose Gleichungen (Whitham-Gleichungen), die als semiklassischer Limes der ursprünglichen Gleichung aufgefasst werden.
| Uhrzeit: | 14:00 - 16:00 |
| Ort: | C5 S7 |
| Gruppe: | Oberseminar Topologie und Differentialgeometrienar Topologie und Differentialgeometrie |
| Einladender: | Bohle, Loose, Radloff |
Dienstag, 05.02.2019: t.b.a.
Arne Gerdes (Göttingen)
t.b.a.
| Uhrzeit: | 16:15 |
| Ort: | S10 |
| Gruppe: | OS Fach- und Hochschuldidaktik Mathematik |
| Einladender: | Cederbaum, Paravicini |
Donnerstag, 07.02.2019: Construction of initial data with monotonous Geroch mass
Dr. Istvan Racz (Wigner RCP)
Consider a smooth three-dimensional manifold $\Sigma$ that is smoothly foliated by topological two-spheres. Choose a smooth flow such that the integral curves of it intersect the leaves of the foliation precisely once. Assume that a smooth distribution of induced two-metrics on the leaves of the foliation is also chosen such that the area of the leaves is non-decreasing. It is shown then that large variety of initial data configurations can be constructed on $\Sigma$ such that the prescribed foliation gets to be an inverse mean curvature foliation, the prescribed flow turns out to be a generalized inverse mean curvature flow and the Geroch mass---defined with respect to the foliation---is guaranteed to be non-decreasing.
| Uhrzeit: | 14:15 |
| Ort: | 7 E 02 (Hörsaalzentrum) |
| Gruppe: | Oberseminar Geometrische Analysis, Differentialgeometrie und Relativitätstheorie |
| Einladender: | Cederbaum, Huisken |