Prof. Dr. Jochen Blath

blath@math.tu-berlin.de


Projects as a project leader

  • CH-AP1

    Interacting stochastic partial differential equations, combinatorial stochastic processes and duality in spatial population dynamics

    Prof. Dr. Jochen Blath

    Project heads: Prof. Dr. Jochen Blath
    Project members: -
    Duration: 01.03.2013 - 30.09.2015
    Status: completed
    Located at: Technische Universität Berlin

    Description

    The method of duality is a mathematical formalism that allows one to establish close connections between two stochastic Markov processes with respect to a class of `duality functions'. If a formal duality is established, it is often possible to study important properties of a `complicated' spatial stochastic system, such as longtime-behaviour or properties of its genealogy, by analysing the properties of a simpler, typically discreteor combinatorial, dual process. This method has been used with great success for many processes in the theory of interacting particle systems and interacting stochastic (P)DEs modeling the evolution of populations (e.g. the stepping stone or the Wright-Fisher model). In the last years, important progress has been achieved. However, there is still no systematic theory of duality (“finding dual processes is something of a black art", A. Etheridge [Eth06] p.519), and many systems of theoretical and practical importance await further analysis. This project has three main objectives. Firstly, we would like to transfer several concrete questions about certain SPDEs to questions about their dual processes (I). Secondly, we are interested in the long-term properties of the dual processes themselves (II). Finally, we aim towards a systematic analysis of the method of duality.

    http://www.dfg-spp1590.de/abstracts.php#27
  • CH-AP2

    Genealogies and inference for populations with highly skewed offspring distributions under further evolutionary forces

    Prof. Dr. Jochen Blath

    Project heads: Prof. Dr. Jochen Blath
    Project members: -
    Duration: 01.10.2012 - 30.06.2018
    Status: running
    Located at: Technische Universität Berlin

    Description

    Multiple merger coalescent modeling and analysis has up to now been mainly focused on neutral, haploid, single-locus set-ups. The central aim of this project is to develop the stochastic models, theoretical results and inference methods required to effectively describe and analyse the observed patterns of genetic variation in sequence data in real populations with skewed offspring distributions under the influence of further evolutionary forces, especially recombination, selection and population structure; in other words, the systematic development of the basics of a `mathematical population genetics for highly variableoffspring distributions'. Given recent progress in DNA sequencing technology, and insight in the limitations of inference methods based single locus set-ups, particular emphasis will be put on realistic diploid multi-locus models and the corresponding statistical machinery for data analysis.

    http://www.dfg-spp1590.de/abstracts.php#5