Mathematisches Kolloquium 2018

  • Prof. Leszek Skrzypczak (Adam Mickiewicz University Poznan, Polen)
    "Compactness of Sobolev embeddings of radial and multi-radial functions: characterizations and applications"
    Abstract: We will discuss the compactness of compact Sobolev embeddings of spaces that consist of radial and block-radial functions. Moreover we describe the asymptotic behaviour of entropy numbers of the embeddings. The numbers describe the compactness in a quantitative way that can be used in the spectral theory of linear operators. In particular, we apply the asymptotic behaviour of entropy numbers to estimate the power of a negative spectrum of Schrödinger type operators with block-radial potentials. This part essentially relies on the Birman-Schwinger principle and Carl’s inequality. 23.05.2018, 17:00 Uhr, HS 228 (Ulmenstr. 69, Haus 3)
    Kolloquiumsleiter: Prof. Dr. Dorothee Haroske
  • Dr. Wolfram Just (Queen Mary University of London)
    "On synchronisation of oscillator networks with propagation delay“
    Abstract: Kuramoto Sakaguchi type models are probably the simplest and most generic approach to investigate phase coupled oscillators. Particular partially synchronised solutions, so called chimera states, have received recently a great deal of attention. Dynamical behaviour of this type will be discussed in the context of time delay dynamics caused by a finite propagation speed of signals.
    02.05.2018, 15:15 Uhr, Raum 427 (Ulmenstr. 69, Haus 3)
    Kolloquiumsleiter: Prof. Dr. Jens Starke
  • Prof. Dr. Wolfgang Härdle (Humboldt-Universität zu Berlin)
    "Dynamic semi-parametric factor model for functional expectiles "
    Abstract: High-frequency data can provide us with a quantity of information for forecasting, help to calculate and prevent the future risk based on extremes. This tail behaviour is very often driven by exogenous components and may be modelled conditional on other variables. However, many of these phenomena are observed over time, exhibiting non-trivial dynamics and dependencies. We propose a functional dynamic factor model to study the dynamics of expectile curves. The complexity of the model and the number of dependent variables are reduced by lasso penalization. The functional factors serve as a low-dimensional representation of the conditional tail event, while the time-variation is captured by factor loadings. We illustrate the model with an application to climatology, where daily data over years on temperature, rainfalls or strength of wind are available.
    26.04.2018, 15:00 Uhr, Seminarraum 120 (Ulmenstr. 69, Haus 3)
    Kolloquiumsleiter: Prof. Dr. A. Meister
  • Prof. Dr. Jan Lang (Ohio State University)
    "Power of generalization"
    Motto: "Etwas allgemein machen, heißt, es denken", W.F.Hegel (1833)
    Abstract: Following the famous quote by Hegel that "To generalize something means to think" we will demonstrate, on a couple of examples, the power of generalization in mathematics. In the first example we introduce Generalized trigonometric functions and present some of their properties and show that they provide us with inside information about some questions in Approximation theory and in study of Non-linear differential equations. In the second example we demonstrate how generalization of the concept of orthogonality, from Hilbert spaces into Banach spaces, bring us a new class of eigenfunctions which will lead us to generalization of Hilbert-Schmidt decomposition.
    18.04.2018, 17:00 Uhr, HS 228 (Ulmenstraße 69, Haus 3)
    Kolloquiumsleiter: Prof. Dr. Peter Takac, Ph.D.
  • Prof. Andrew Thomason (University of Cambridge)
    "Containers in combinatorics"
    Abstract: A hypergraph with vertex set, say, {1,2,...,n} is a collection of subsets of the vertex set of some fixed size - these subsets are called edges. For example, the subsets might be all triples that form an arithmetic progression. An independent set in the hypergraph is a subset of the vertices that contains no edge - in the example, it would be a set of integers containing no 3-AP. It has recently been discovered that the independent sets in any hypergraph must be structured in some way: they are all contained within one of a small collection of "independent-like" subsets. We shall discuss this discovery and its applications, with examples from arithmetic and from graph theory.
    24.01.2018, 15:15 Uhr, HS 228 (Ulmenstr. 69, Haus 3)
    Kolloquiumsleiter: Dr. rer. nat. habil. Peter Wagner
  • Prof. Dr. rer. nat. Pavel Drabek, Dr.Sc. (Westböhmische Universtität Pilsen)
    "Convergence to travelling waves in Fisher’s population genetics model with a non-Lipschitzian reaction term"
    Abstract
    15.01.2018, 17:00 Uhr, HS 228 (Ulmenstr. 69, Haus 3)
    Kolloquiumsleiter: Prof. Dr. Peter Takac, Ph.D.