Successfully completed projects

Financed by others

  • GV-AP12

    SDModels - Structured Discrete Models as a basis for studies in geometry, numerical analysis, topology, and visualization

    Prof. Günter M. Ziegler

    Project heads: Prof. Günter M. Ziegler
    Project members: -
    Duration: 01.07.2010 - 30.06.2015
    Status: completed
    Located at: Freie Universität Berlin

    Description

    This project was successfully completed June 2015, after five years of intensive work, three very productive SDModels workshops, and lots of other activities. It has produced numerous successes, advanced the careers of the students and scientists involved, and produced a lot of output - a large part of this documented in scientific publications, many more papers are still under review and on the way to publication. We are happy for all the support and opportunities we had with this project, and grateful to ERC and its reviewers and administrators for making it possible. The work by SDModels is documented on these web pages. They will not be updated any more after December 2015: Please see the web pages of the scientists involved for their continuing work.

    The research of the SDModels project has connected traditionally quite distant fields of current mathematical research via common or structurally similar discrete (mostly: geometric) models. We thus made substantial contributions to mathematical research, by highlighting, developing, and exploiting theory for common structures and structural similarities that occur in problems/theories from diverse mathematical application areas. This involved, in particular, the areas of
    1. Discrete Geometry
    2. Discrete Differential Geometry
    3. Mesh Generation/Numerics of PDEs
    4. Topology, Topological Combinatorics
    5. Simplicial Quantum Gravity

    The work in the project was concentrated in three Focus Areas, namely
    • Focus Area 1: High-complexity Geometry
    • Focus Area 2: Delaunay Geometry: Polyhedral models with circle/sphere patterns
    • Focus Area 3: Topological connectivity and diameter of Discrete Structures


    http://www.mi.fu-berlin.de/math/groups/discgeom/projects/ERC/index.html
  • GV-AP19

    Topological microstructure analysis of metal and steel grains

    PD Dr. Frank Lutz

    Project heads: PD Dr. Frank Lutz
    Project members: -
    Duration: 01.03.2014 - 31.03.2016
    Status: completed
    Located at: Technische Universität Berlin

    Description



  • GV-AP2

    Integrating discrete geometries and finite element spaces

    Prof. Dr. Konrad Polthier

    Project heads: Prof. Dr. Konrad Polthier
    Project members: -
    Duration: 01.07.2012 - 30.06.2016
    Status: completed
    Located at: Freie Universität Berlin

    Description

    Finite element methods are in every day use in engineering and modelling. The main idea with finite elements is to discretize objects such as machine parts or architectural elements in order to then simulate the movement and behaviour of these objects via discrete computations. Project A04 aims to link experiences from those applications of scientific computing with ideas from discrete geometry to improve the integration of technologies.

    http://www.discretization.de/en/projects/A04/
  • GV-AP3

    Riemannian manifold learning via shearlet approximation

    Prof. Dr. Gitta Kutyniok

    Project heads: Prof. Dr. Gitta Kutyniok
    Project members: -
    Duration: 01.01.2013 - 30.06.2016
    Status: completed
    Located at: Technische Universität Berlin

    Description

    Applied harmonic analysis provides powerful methodologies to approximate geometric objects, which might be given as a Riemannian manifold itself or as an approximating point cloud. The main tools are specifically designed representation systems such as shearlets. These systems are of a multiscale type, thus an approximation process provides different resolution levels. One might ask: "Which resolution level allows detection of which geometric properties, such as curvature or torsion?" Project A10 aims to analyze such relations between approximations and learning of geometrical properties.

    http://www.discretization.de/en/projects/A10/
  • GV-AP4

    Interactive tools for research and demonstration

    Prof. Dr. Ulrich Pinkall / Prof. John Sullivan

    Project heads: Prof. Dr. Ulrich Pinkall / Prof. John Sullivan
    Project members: -
    Duration: 01.07.2012 - 30.06.2016
    Status: completed
    Located at: Technische Universität Berlin

    Description

    Today, software for analyzing and visualizing mathematical objects is an important tool for getting a grip on the mathematical matter one is exploring. There is already a lot of expertise in the SFB/Transregio with software in different fields of differential and combinatorial geometry. Project C01 aims to bring this experience together, for instance by building generic libraries for visualization and 3D-rendering or by enhancing the interoperability of the existing software projects.

    http://www.discretization.de/en/projects/C01/
  • GV-AP7

    Modeling synaptic connectivity in anatomically realistic neural networks

    Hon Prof. Hans-Christian Hege

    Project heads: Hon Prof. Hans-Christian Hege
    Project members: -
    Duration: 01.07.2014 - 31.12.2015
    Status: completed
    Located at: Konrad-Zuse-Zentrum für Informationstechnik Berlin

    Description

    The goal of the NeuroConnect project is
    • to generate anatomically realistic 3D neural network models,
    • to provide tools to analyze such models and
    • to extract information for numerical simulations of neural activity, particularly the synaptic connectivity.

    This requires the development of new methods to effectively specify, visualize, and quantify the information of interest in these potentially large (>500k neurons) and complex neural networks, as well as efficient data structures to represent and process this data. Methods to extract the anatomical data underlying the network model and the modeling approach have been developed in the past Cortex In Silico project.

    http://www.zib.de/projects/modeling-synaptic-connectivity-anatomically-realistic-neural-networks

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