• 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
  Now 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):

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

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

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

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

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

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

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

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

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