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Vorträge in der Woche 27.11.2017 bis 03.12.2017

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Montag, 27.11.2017: Massively parallel computations in algebraic geometry

Dr. Janko Böhm (TU Kaiserslautern)

The design and implementation of parallel algorithms is still a fundamental task in computer algebra. In high performance numerical simulation, massively parallel computations relying on transparent environments for separating computation and coordination have been a success story for many years. We explore the potential of one of these environments in the context of computer algebra. To do so, we combine two well-established systems: the computer algebra system Singular for polynomial computations and the workflow management system GPI-Space, which relies on Petri nets as its mathematical modeling language. The result is a framework for massively parallel computations in commutative algebra and algebraic geometry. As a first test case for this framework, we have modeled and implemented a new algorithm for deciding smoothness of algebraic varieties - a task many constructions in algebraic geometry rely on. Our algorithm combines the termination criterion of Hironaka's approach for resolution of singularities with the Jacobian criterion. We discuss the performance, and the potential of the framework in further applications. This talk is based on joint work with Wolfram Decker, Anne Frühbis-Krüger, Franz-Josef Pfreundt, Mirko Rahn and Lukas Ristau.

Beginn: 17:17 Uhr
Ort:N 14
Einladender:Hannah Markwig

Donnerstag, 30.11.2017: The null Penrose inequality and the shell version in Minkowski

Dr. Alberto E. Soria Marina (University of Salamanca)

The Penrose inequality establishes a lower bound for the total mass of a space- time in terms of the area of certain surfaces. It was originally formulated in the early seventies by Penrose and is a very challenging problem in mathematical relativity. Its validity would give strong support to the weak cosmic censorship conjecture. A very interesting case is the so called null version, in which the surface is embedded in a null hypersurface that extends regularly to past null infinity. The shell version is obtained by rewriting the null general inequality in terms of the geometry of the Minkowski spacetime. I prove the validity of the null and the shell version in some cases, and obtain two new Penrose-type inequalities.

Beginn: 14:15 Uhr
Gruppe:Oberseminar Geometrische Analysis, Differentialgeometrie und Relativitätstheorie
Einladender:Cederbaum, Huisken

Donnerstag, 30.11.2017: Averaging of nonlinear Schrödinger equations with strong confinement and rotation

Prof. Christof Sparber (University of Illinois at Chicago)

We consider a class of nonlinear Schro?dinger equations (NLS) subject to strong anisotropic confining forces by, either, electric, or constant magnetic fields. Introducing a small adiabatic parameter, we study the limit as this parameter tends to zero. Using a high-frequency averaging technique we rigorously derive effective lower dimensional NLS type models. In particular we obtain a derivation of the LLL equation (“lowest Landau level equation”) as a limiting model.

Beginn: 16:15 Uhr
Gruppe:OS MaPhy
Einladender:Hainzl, Keppeler, Porta, Teufel, Tumulka

Donnerstag, 30.11.2017: Rough paths and stochastic calculus (a digest)

Antoine Hocquet, Ph.D. (TU Berlin)

Stochastic differential equations of the form du = f(u) dt + g(u) dB, T>t>0, u(0) given, where B is an irregular signal (e.g. the Brownian motion), usually appeal to probabilistic arguments, such as Itô integration, with a reference to a filtered probability space. Despite its success, the latter approach limits the possible range of equations to deal with, since they have to be "compatible'' with respect to the filtration. Also, it is well-known that the solution mapping B -> u lacks continuity, in any Banach space which supports the Brownian motion. Following the lines of Lyons '97 and Gubinelli '04, I will introduce a rough path approach to solve such equations, and explain how it allows to deal with the previous problems.

Beginn: 16:15 Uhr
Gruppe:Oberseminar Stochastik
Einladender:Möhle, Prohl, Teufl, Zerner