• Wolfgang Hackbusch (1999 - 2014, retired director)
  Numerical solution of partial differential equations and integral equations, Multi-grid methods, Boundary element methods

• Stefan Müller (1996 - 2008, former director)
  Mathematical foundations of materials science, microstructures, micromagnatism, continuum mechanics, singular perturbations, non-linear partial differential equations and the calculus of variations
  Ensuing position at: Hausdorff Center for Mathematics Bonn (Germany), see homepage

• Eberhard Zeidler (1996 - 2007, †)
  Non-linear partial differential equations, non-linear functional analysis, classical and modern mathematical physics, selected questions of mathematical chemistry and mathematical biology

Following the links you will go to the homepages of the heads of former research groups (all external):

• Nihat Ay (2005 - 2021)
  Information Theory of Cognitive Systems
  Ensuing position at: Hamburg University of Technology (Germany), Institute for Data Science Foundations, see homepage

• Lehel Banjai (2008 - 2012)
  Numerical Methods for Time Domain Acoustics and Electromagnetics
  Ensuing position at: Heriot-Watt University (Edinburgh, Scotland), School of Mathematical & Computer Sciences, see homepage

• Antonio DeSimone (1998 - 2003)
  Multi-scale phenomena in materials
  Ensuing position at: Scuola Internazionale Superiore di Studi Avanzati (SISSA) Trieste (Italy), see homepage

• Nicolas Dirr (2004 - 2007)
  Mathematical Models for Materials
  Ensuing position at: Cardiff University (United Kingdom), see homepage

• Peter Hornung (2011 - 2013)
  Emmy Noether Group: Geometric Analysis in the Applied Sciences
  Ensuing position at: Hausdorff Center for Mathematics Bonn (Germany), see homepage

• Mateusz Michałek (2017 - 2020)
  Combinatorial Algebraic Geometry
  Ensuing position at: Universität Konstanz, see homepage

• Angkana Rüland (2017 - 2020)
  Rigidity and Flexibility in PDEs
  Ensuing position at: University Heidelberg (Germany), see homepage

• Artem Sapozhnikov (2012 - 2017)
  Random spatial processes
  Ensuing position at: University Leipzig (Germany), see homepage

• Matthias Schwarz (1999 - 2000)
  Symplectic Geometry and Hamiltonian Dynamical Systems
  Ensuing position at: University Leipzig (Germany), see homepage

• Emanuele Spadaro (2011 - 2016)
  Geometric Measure Theory and Applications
  Ensuing position at: University Leipzig (Germany), see homepage

• Angela Stevens (2001 - 2007)
  Mathematical Biology
  Ensuing position at: University Münster (Germany), see homepage

• Johannes Zimmer (2003 - 2004)
  Emmy Noether Group
  Ensuing position at: BATH (United Kingdom), see homepage