 Souganidis was a postdoc in 1984–1985 at the University of Minnesota's Institute for Mathematics and its Applications and was at the Institute for Advanced Study in 1988 and 1990.After holding professorships at Brown University, the University of Wisconsin–Madison, and the University of Texas at Austin, he became in 2008 the Charles H. Swift Distinguished Service Professor in Mathematics at the University of Chicago.He has held visiting positions at academic institutions in Italy, Japan, Greece, France, the UK, and Sweden.