He has held visiting positions at Cornell University, the University of Hawaii, the Isaac Newton Institute of the University of Cambridge, the Mathematical Sciences Research Institute in Berkeley, California, and the Fields Institute in Toronto, Canada.
Trotman has directed eleven PhD theses.
Among his research students are Patrice Orro, Karim Bekka, Claudio Murolo, Georges Comte, Dwi Juniati and Guillaume Valette.Trotman was Director of the Graduate School in Mathematics and Computing of Marseilles from 1996 to 2004, and was an elected member of the CNU (the French National University Council) from 1999 until 2007.