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Institute of Mathematics of the Romanian Academy
UPENN Math Department : this is the place where I got my Ph.D. from.
UIC Math Department : I spent 2 years as a Postdoc here.
Courant Institute, NYU : I was a Postdoc/Courant Instructor here during the Spring 2006 semester, and a Research Fellow during 09/2007-08/2009.
Problems in algebraic topology: Poincare duality, spectral sequences, characteristic classes (a good practice for the qualifying exam in algebraic topology).