Mathematisches Forschungskolloquium 2023

Das Forschungskolloquium richtet sich an ein breites mathematisches Publikum. Es soll die Diskussionen über die mathematischen Spezialisierungen der verschiedenen Arbeitsgruppen hinaus am Institut fördern. Außerdem sollen auch Studierende (Master-Studierende und fortgeschrittene Bachelor-Studierende) durch das Kolloquium die Gelegenheit erhalten, sich über aktuelle Themen der Mathematik zu informieren.

  • Dr. Rainer Klages (Queen Mary University of London)
    "Transition to anomalous dynamics in simple random maps"
    Abstract: "A random dynamical system consists of a setting where different types of dynamics are generated randomly in time. Here we consider as a simple example a piecewise linear one-dimensional map on the unit interval, where an irregular or a regular dynamic is randomly selected at each discrete time step for determining the outcome at the next time step. By continuously varying as a control parameter between zero and one the sampling probability to select the one or the other dynamic, the completely irregular, respectively regular dynamics are recovered as limiting cases. Hence, there must be a transition between these two states, where the combined dynamics exhibit intermittency. In my talk I will explore this transition in detail. I will show that there is a critical sampling probability at which the dynamic becomes anomalous, in the sense that the invariant density is non- normalisable, there is loss of ergodicity, and the correlations decay as a power law. I will also explore the impact of this transition onto the diffusive properties of a related lifted map."
    18. Dezember 2023, 14:00 Uhr, Raum 222 (Ulmenstr. 69, Haus 3)
    Kolloquiumsleiter: Dr. Wolfram Just
  • Fr. PD Dr. Isabelle Schneider (FU Berlin)
    Thema: " Symmetry groupoids of dynamical systems"
    Symmetries described by group transformations help immensely in our task to qualitatively characterize solutions of dynamical systems - providing that they exist. In this talk based on my habilitation thesis, we significantly enlarge the class of dynamical systems which can be studied by symmetry methods, moving our focus from groups to groupoids as the underlying algebraic structure describing symmetry. Building on the groupoid framework, we fundamentally generalize the notion of equivariance and equivariant bifurcation theory. We will also outline first applications in modelling and control of dynamical systems.
    Donnerstag, 14.12.2023, 14:00 Uhr, Ulmenstr. 69, Haus 3, Raum 221
  • Ing. Ph. D. Lukas Kotrla (Universität Pilsen, Tschechien)
    Thema: "Nonuniqueness and multi-bump solutions in parabolic problems with the $p$-Laplacian"
    The validity of the weak and strong comparison principles for degenerate parabolic partial differential equations with the p-Laplace operator Delta_p is investigated for p > 2. This problem is reduced to the comparison of the trivial solution (≡ 0, by hypothesis) with a nontrivial nonnegative solution u(x,t). Auch interessierte Studierende sind herzlich eingeladen.
    Mittwoch, 06.12.2023, 16:00 Uhr, Ulmenstr. 69, Haus 3, HS 125

  • Dr. Rainer Klages (Queen Mary University of London)
    "Stochastic modelling of biological motion: sea turtles, bumblebees and crawling cells"
    Abstract: "I will present three examples for statistical experimental data analysis of biological motion, with the aim to construct stochastic models reproducing the dynamics. First I consider the paths of loggerhead sea turtles foraging in front of the coast of West Africa. Then I study the flight paths of bumblebees searching for nectar by changing environmental conditions in a laboratory experiment. Finally I analyse experimentally observed trajectories of crawling biological cells. In all three cases stochastic models are constructed based on the data, which deviate from simple Brownian motion. These models are generalised Langevin equations and related stochastic processes, partially generating anomalous dynamics."
    25. Oktober 2023, 15:15 Uhr, HS 326/327 (Ulmenstr. 69, Haus 3)
    Kolloquiumsleiter: Dr. Wolfram Just