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This is a survey paper based on the author's lectures given at IMPAN in December 2013. We will discuss recent results on the restriction and rigidity problems. The purpose of the lectures was to develop a more geometric approach to the study of isotropic flag varieties. As an illustration of the techniques, we compute the map induced in cohomology of the inclusion of and in via an explicit sequence of rational equivalences. We also discuss applications to classifying representatives of Schubert classes.