Research Fields

  • High-Dimensional PDEs
  • Low-Rank Approximation
  • Adaptive Approximation
  • Reduced Basis Methods
  • Wavelets


  • Mazen Ali: Low-Rank Approximability and Entropy Area Laws for PDEs (arXiv).
  • Mazen Ali, Anthony Nouy: Singular Value Decomposition in Sobolev Spaces (arXiv).
  • Mazen Ali, Karsten Urban: HT-AWGM: A Hierarchical Tucker-Adaptive Wavelet Galerkin Method for High Dimensional Elliptic Problems (arXiv).
  • Mazen Ali, Kristina Steih, Karsten Urban: Reduced Basis Methods with Adaptive Snapshot Computations. Advances in Computational Mathematics, Volume 43, Issue 2, pp 257-294 (2017). DOI:
  • Mazen Ali, Karsten Urban: Reduced Basis Exact Error Estimates with Wavelets. In: Karasözen B., Manguoğlu M., Tezer-Sezgin M., Göktepe S., Uğur Ö. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2015. Lecture Notes in Computational Science and Engineering, vol 112. Springer, Cham (2016). DOI:


  • Winter term 2019/2020: Numerical Finance (exercise supervisor).
  • Summer term 2019: Reduced Basis Methods (exercise supervisor).
  • Winter term 2018/2019: Numerics of Elliptic Partial Differential Equations (exercise supervisor).
  • Summer term 2018: Numerical Finance (exercise supervisor).
  • Winter term 2017/2018: Numerics of Elliptic Partial Differential Equations (exercise supervisor).
  • Summer term 2017: Seminar Reduced Basis Methods (seminar supervisor).
  • Winter term 2016/2017: Wavelets in Image Compression and Numerical Simulation (exercise supervisor).
  • Summer term 2016: High Performance Computing 2 (exercise supervisor).
  • Winter term 2015/2016: Numerics of Partial Differential Equations (exercise supervisor).
  • Summer term 2015: Seminar Numerics of Partial Differential Equations (seminar supervisor).
  • Winter term 2014/2015: Scientific Working in CSE (exercise supervisor).
  • Spring term 2014: Calculus 2 for Engineers (exercise supervisor). Missouri S&T.
  • Fall term 2013: Financial Mathematics (exercise supervisor). Missouri S&T.

Conferences and Research Stays

  • Low-Rank Approximability and Entropy Area Laws for PDEs. 26 September 2019, Seminar on Applied Mathematics at University of Nantes (France). Talk given.
  • 16 September - 11 October 2019, research stay with Anthony Nouy at University of Nantes (France).
  • Innovative Approaches to the Numerical Approximation of PDEs. 1-7 September 2019, Mathematisches Forschungsinstitut Oberwolfach (Germany). Talk given.
  • Low-Rank Optimization and Applications. 1-5 April 2019, MPI MiS Leipzig (Germany). Poster presented.
  • Low-Rank Approximability and Entropy Scaling for Eigenfunctions of a PDE. 6 March 2019, Seminar on Nonlinear Algebra at MPI MiS Leipzig (Germany). Talk given.
  • Modelling, Analysis and Simulation of Molecular Systems. 25-26 October 2018, FU Berlin (Germany). Talk given. 
  • Analysis and Computation in High Dimensions. 1-5 October 2018, HCM Bonn (Germany). Poster presented.
  • Model Reduction of Parametrized Systems IV. 10-13 April 2018, Nantes (France). Poster presented.
  • 18-19 December 2017, short research visit with Rob Stevenson at the University of Amsterdam (Netherlands).
  • 28 August - 24 September 2017, research stay with Anthony Nouy at Centrale Nantes (France).
  • Aachen Conference on Computational Engineering Science. 27-28 July 2017, Aachen (Germany). Poster presented.
  • Wavelet and Tensor Methods for Partial Differential Equations. 3-5 May 2017, Berlin (Germany).
  • 13 February - 10 March 2017, research stay with Anthony Nouy at Centrale Nantes (France).
  • 4-th International Workshop "Analysis, Geometry and Probability". 26 September - 2 October 2016, Moscow (Russia). Talk given.
  • Winter School on Hierarchical Matrices. 22-26 February 2016, Kiel (Germany).
  • Reduced Basis Summer School 2015. 14-18 September 2015, Konstanz (Germany). Talk given.
  • Final Conference of SPP 1324 "Mathematical Methods for Extracting Quantifiable Information from Complex Systems". 24-28 November 2014, Marburg (Germany).