Universität Bonn

Hausdorff School: "Low-rank Tensor Techniques in Numerical Analysis and Optimization"

 18 April 2016 to 22 April 2016

Mathematik-Zentrum, Lipschitz Lecture Hall, Endenicher Allee 60, Bonn

Organizers: André Uschmajew (Universität Bonn)

Description: Low-rank tensor approximation is an established tool in signal processing and data analysis to decompose multilinear data beyond standard matrix principal component analysis. In recent years its application to modern large scale problems has become an active area of research. A different motivation for the development of low-rank tensor techniques comes from the "curse of dimensionality” after discretization of high-dimensional functions as they arise, for example, in quantum physics or uncertainty quantification. When the number of variables becomes unmanagebly large, traditional numerical methods for solving (partial) differential, integral, or eigenvalue equations are severely limited in their application.

The transition from low-rank matrix to low-rank tensor approximation involves many surprisingly hard challenges and open problems on the theoretical and practical level. To investigate these problems, it is important to combine the developments from different fields within numerical mathematics and optimization that aim at understanding and developing low-rank tensor techniques. In particular, there is a fruitful interaction of theoretical tools from different mathematical branches, such as approximation theory, algebraic/differential geometry, linear algebra, and numerical analysis, on the one side, and there are various application areas in big data, quantum physics, computational chemistry, or computer science, on the other side.

This Hausdorff School is intended for graduate and postdoctoral students who are interested in classical results and recent developments in low-rank tensor approximation, and wish to acquire modern research tools to work in the field. Particular focus will be on high-dimensional numerical tensor calculus, and low-rank optimization methods.

Participants of the Hausdorff School © HIM

Lecture Series by: 

  • Lars Grasedyck (RWTH Aachen)
    • Hierarchical Tucker format
    • Blackbox / Cross approximation
    • Outlook, applications and discussion
  • Bart Vandereycken (Université de Genève)
    • Tensor trains and matrix product states
    • Riemannian optimization for tensors
    • Quantized tensor trains
  • André Uschmajew (Universität Bonn)
    • Tensor product of Hilbert spaces
    • Low-rank approximability


Period of stay
Moritz August Technical University of Munich
Oleg Balabanov Ecole Centrale de Nantes
Martijn Boussé KU Leuven
Daan Camps KU Leuven
Otto Debals KU Leuven
Reinier Doelman TU Delft
Simon Etter University of Warwick
Lars Grasedyck RWTH Aachen
Behnam Hashemi Mathematical Institute, University of Oxford
Benjamin Huber Technische Universitaet Berlin
Ben Jeuris KU Leuven
René Kehl TU Berlin
Kristin Kirchner Chalmers University of Technology
Erna Begovic Kovac University of Zagreb
Benjamin Kutschan TU Berlin
Maxim Kuznetsov Lomonosov Moscow State University
Christian Kümmerle Technische Universität München
Dana Lahat GIPSA-Lab
Alexander Litvinenko KAUST
Dimitrios Loukrezis TU Darmstadt
Johannes Maly TU München
Davide Palitta Università di Bologna
Lana Perisa University of Split, Croatia
Max Pfeffer Technische Universitaet Berlin
Duong Luu Trung Pham University of Luxembourg
Luis Garcia Ramos Technische Univiersitaet Berlin
Rishi Relan Vrije Universiteit Brussel
Emil Ringh KTH Royal Institute of Technology
Erik Marc Schetzke Universität Oldenburg
Carlos Echeverria Serur Technische Universität Berlin
Baptiste Sinquin TU Delft
Bedrich Sousedik University of Maryland, Baltimore County
André Uschmajew Universität Bonn
Bart Vandereycken University of Geneva
Hanna Walach Tuebingen University
Sebastian Wolf Technische Universität Berlin
Chengpu Yu Delft University of Technology
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