Wlater is a professor emeritus at the department of mathematics of the University of Leuven (KU Leuven) since October 1, 2023. He was the head of the department of mathematics from 2006 to 2015 and he is a member of the section of Analysis. Up to September 30, 2000 he was a Research Director (onderzoeksdirecteur) of the Belgian National Fund for Scientific Research, now Research Foundation – Flanders (FWO). He was chair of the SIAM activity group Orthogonal Polynomials and Special Functions from 2014 to 2019.