News & Activities

• Research Topic on High-Performance Tensor Computations in Scientific Computing and Data Science
  in Frontiers in Applied Mathematics and Statistics. Submission deadline October 1, 2021.
   
• Workshop: Hierarchical Numerical Methods for PDEs
  September 28-29, 2020 at MPI Leipzig
   
• Workshop: Mathematical Foundations and Algorithms for Tensor Computations
  May 3-7, 2021 at IPAM (now online)
  Part of the IPAM Long Program: Tensor Methods and Emerging Applications to the Physical and Data Sciences (March 8 - June 11, 2021).
   
• GAMM AG Workshop Computational and Mathematical Methods in Data Science (COMinDS 2020)
  September 10-11, 2020 in Leipzig (online)
   
• Mathematics of Data Initiative at MPI MiS
  Please check for the regular seminars, courses and workshops.
   

Research

The research in our group focuses on low-rank matrix and tensor approximation, with emphasis on numerical tensor calculus, nonlinear optimization methods, underlying approximability principles, as well as algebraic and geometric foundations. Our goal is to obtain a deeper understanding of low-rank models and methods, and their successful use in scientific computing and modern applications. Some keywords:

• Tensors: geometry of low-rank varieties, tensor networks, higher-order singular values, tensor product operators
• Approximation: functional analytic foundations, approximation rates, singular value estimates, spectral and nuclear norm
• Optimization: block coordinate methods, truncated iterations, Riemannian optimization, rank adaptivity, optimization landscape
• Applications: high-dimensional linear equations and eigenvalue problems, signal processing, dynamical low-rank approximation