Vorträge in der Woche 09.02.2015 bis 15.02.2015
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Mittwoch, 11.02.2015: Zur Störungstheorie von Generatoren
Miriam Bombieri
Nach einer Einfürung in die Problematik der Störungstheorie von Generatoren, stellen wir einen allgemeinen Störungssatz und einige Anwendungen vor.
| Uhrzeit: | 10:15 |
| Ort: | S11 |
| Gruppe: | Oberseminar Mathematische Physik |
| Einladender: | Teufel |
Donnerstag, 12.02.2015: Multilevel Monte Carlo methods and stochastic partial differential equations
Andrea Barth (Universität Stuttgart)
In ample applications of partial differential equations, the input parameters are uncertain or there is some intrinsic noise in the system. The said uncertainty may be modeled by a (infinite dimensional) random variable. This in turn implies that the solution to the partial differential equation is also a (infinite dimensional) random variable. In other words, the solution is at every point in the spacial (and temporal) domain not given by a value but by a measure. In this talk I give an introduction to multilevel Monte Carlo methods, which allow for an efficient approximation of the mentioned measures. Additionally, I reflect on some advantages and disadvantages of multilevel Monte Carlo methods and present several numerical simulations.
| Uhrzeit: | 14:15 |
| Ort: | N 14 |
| Gruppe: | Oberseminar Numerik |
| Einladender: | Lubich, Prohl |
Donnerstag, 12.02.2015: Mean-Field Limes und Dimensionsreduktion
Johannes von Keler
In meinem Vortrag werden bosonische Vielteilchensysteme in drei Raumdimensionen betrachtet, die durch ein äußeres Potential in einer bzw. zwei Raumdimensionen stark eingeschränkt sind. Es wird gezeigt, dass solche N-Teilchensysteme durch eine effektive Einteilchengleichung approximiert werden können, wobei die effektive Gleichung aufgrund des starken äußeren Potentials zwei- bzw. eindimensional ist. Es wird bewiesen, dass diese Approximation im thermodynamischen Limes N ! 1 exakt wird. Darüber hinaus wird die Konvergenzgeschwindigkeit diskutiert, die im Besonderen für die Anwendbarkeit der Ergebnisse auf physikalische Experimente von Bedeutung ist.
| Uhrzeit: | 14:15 |
| Ort: | N 16 |
| Gruppe: | Promotionsvortrag |
| Einladender: | Teufel |
Donnerstag, 12.02.2015: On terminal Fano 3-folds with 2-torus action
Michele Nicolussi (Universität Tübingen)
We classify the terminal Fano threefolds of Picard number one that come with an effective action of a two-torus. Our approach applies also to higher dimensions and more general settings: to any Fano variety with a complete intersection Cox ring we associate its "anticanonical complex'', which is a certain polyhedral complex living in the lattice of one parameter groups of an ambient toric variety. For resolutions constructed via the tropical variety, the lattice points inside the anticanonical complex control the discrepancies. This leads, for example, to simple characterizations of terminality and canonicity. We give a closer look at the various tools and strategies that lead to the above-mentioned classification.
| Uhrzeit: | 16:15 |
| Ort: | N 16 |
| Gruppe: | Oberseminar Algebraische Geometrie |
| Einladender: | Batyrev, Hausen |
Donnerstag, 12.02.2015: Derivation of the semiclasscal Schrödinger equation from QED
Prof. Dr. Peter Pickl (LMU Muenchen)
It is well known, that the interaction of a charge with photons that are in a coherent state can in good approximation be described classically. Of course a coherent state is only an idealization. But in which sense are the photons which are naturally created by a system of many charges close to a coherent state? And is this sense sufficient to explain classical behaviour? In the talk I will give an answer to these questions. I will discuss the solutions of the Pauli-Fierz equation, starting with a condensate of charges and no photons. I will show that the photons created during time evolution are in fact close to coherent states such that their interaction with another charge can be described semiclassically, i.e. by the Schrödinger equation where the A-field is treated classically. I will also show, that A is a solution of Maxwell's equations.
| Uhrzeit: | 16:30 |
| Ort: | M1 (N14) |
| Gruppe: | Oberseminar Mathematische Physik |
| Einladender: | Teufel |