In the academic year 1998-1999, he was supported by a Pisart research fellowship from the University of Liège. From 1999 to 2003, he was a Research Fellow with the Belgian National Fund for Scientific Research (Aspirant du FNRS). In 2003-2005, he was a Postdoctoral Associate with the School of Computational Science at Florida State University. He was a Research Fellow with Peterhouse, University of Cambridge (UK) in 2005-2006. He was a visitor with Monash University, Australia (2001), the University of Würzburg, Germany (2002), Sandia National Laboratories, USA (2005), the Australian National University (2009), and Université Paul Sabatier, Toulouse, France (2010).
Dr Absil's major research area is numerical optimization, with particular interests in numerics on manifolds, linear and nonlinear programming algorithms, and biomedical applications. He was awarded the 2000 IBRA-BIRA prize for his Graduate Thesis (analysis of cardiological signals) and the 2002 SIAM Student Paper Prize for the paper ``A Grassmann-Rayleigh Quotient Iteration for Computing Invariant Subspaces´´.