Abstract: Exceptional collections in derived categories of coherent sheaves have a long history going back to the pioneering work of A. Beilinson. After recalling the general setup, I will concentrate on some very recent developments inspired by the homological mirror symmetry. Namely, I will define residual categories of Lefschetz decompositions and discuss a conjectural relation between the structure of quantum cohomology and residual categories. I will illustrate this relationship in the case of some isotropic Grassmannians. This is a joint work with Alexander Kuznetsov.
Attention: Unusual time and place