He attended the Royal Conservatories in Antwerp and in Brussels, and later studied with Igor Markevitch and Nadia Boulanger.
From 1994 to 2002, he was music director of the National Autonomous University of Mexico Philharmonic Orchestra (Orquestra Filarmónica de la UNAM).
In May 2009, Zollman accepted the Associate Professor of Music and Director of Orchestral Studies position at the Carnegie Mellon University School of Music in Pittsburgh, Pennsylvania.
In September 2011 he added the position Principal Guest Conductor of the Czech Radio Symphony Orchestra to his activities, and he occupied the same position at the Pilsen Philharmonic Ochesta from 2014 onward.
Over the years, Zollman has guest conducted concerts with more than 150 different orchestras on the 5 continents.