Vorträge in der Woche 12.01.2015 bis 18.01.2015

Montag, 12.01.2015: Marginal Probability Density in the Real Wishart Model: Exact Results

Prof. Dr. Thomas Guhr (Duisburg-Essen)

When analyzing time series, the correlations between them are of particular importance. The Wishart model is based on random matrices and provides a benchmark for the statistical analysis of these correlations. The marginal probability (or eigenvalue) density in this model is of considerable practical and theoretical interest. For complex time series and correlation matrices, the marginal probability density is known exactly. In the more important real case, a fundamental mathematical obstacle made it forbiddingly complicated to obtain exact results. This is related to harmonic analysis in certain symmetric spaces and to spherical functions as introduced by Gelfand and by Harish-Chandra.<br> <br> We use the supersymmetry method to fully circumvent this problem. We present an exact formula for the marginal probability density in the real case in terms of twofold integrals and finite sums. The result can be viewed as a resummation of a series of matrix-valued Jack polynomials in a non-trivial case.

Dienstag, 13.01.2015: Stochastic Quantum Scattering: Recent Exact Results and Comparison with Experiments

Prof. Dr. Thomas Guhr (Duisurg-Essen)

A major part of our knowledge about quantum systems stems from scattering experiments. In many cases, the complexity of the problem calls for a statistical modelling. In the so-called Heidelberg approach, the Hamiltonian of the system at which the projectiles are scattered is modelled as a random matrix. Years ago, moments of the scatting matrix elements were calculated using supersymmetry. However, the full distribution (probability density function) of the off-diagonal sacttering matrix elements resisted an exact analytical treatment ever since the Heidelberg approach was introduced. We put forward a variant of the supersymmetric non-linear sigma model and completely solve this problem.

Dienstag, 13.01.2015: Neuronale Plastizität und Lernen: Beispiele Klinischer Extrem-Situationen

Prof. Niels Birbaumer (Tübingen)

Dienstag, 13.01.2015: Grundzüge der Seibert-Witten-Floer-Homologie, Teil II

Jonathan Walz (Tübingen)

Dienstag, 13.01.2015: Kusnetsov Quotient with nonstandard functions

Martin Laur (Tübingen)

Donnerstag, 15.01.2015: TBA

Dr. David Fajman (Universität Wien)

Donnerstag, 15.01.2015: The Einstein-flow on the 2-sphere

Dr. David Fajman (Universität Wien)

We study the Einstein-flow on the 2-sphere coupled to the massive Vlasov equation. We construct isotropic, future complete, non-vacuum solutions, which have no vacuum counterparts and study their nonlinear stability problem. The results illustrate a feature of the Einstein-Vlasov system in 2+1 dimensions, which "decouples" the spatial topology from the future asymptotic behavior of the solutions.

Donnerstag, 15.01.2015: Forschendes Lernen im Mathematikunterricht

Prof. Dr. Brigitte Lutz-Westphal (Freie Universität Berlin)

Wenn Mathematikunterricht ein authentisches Bild von Mathematik vermitteln soll, muss er auch forschende Ansätze enthalten. Was genau ist mit forschendem Lernen im Mathematikunterricht gemeint? Welche Rahmenbedingungen müssen dafür geschaffen werden? Was kann ein forschender Unterricht inhaltlich leisten und was nicht? Verschiedene Unterrichtsprinzipien, z.B. das dialogische Lernen und das entdeckende Lernen, verbinden sich dabei zu einem Konzept, das den Schülerinnen und Schülern neue Horizonte eröffnen kann und nachhaltigere Wissensstrukturen schafft. Im Vortrag wird sowohl aus der Arbeit mit Lehramtsstudierenden als auch aus der Begleitung des Projekts "Mathe.Forscher" der Stiftung Rechnen berichtet.