Описание: I am going to speak about automorphisms of Fano varieties (with applications to finite subgroups of Cremona groups). I will start with simple examples of "interesting" automorphism groups of Fano varieties in dimension 2 and 3. Then I will explain the classification of smooth Fano 3-folds according to Iskovskikh and Mukai , and outline a recipe of describing automorphisms in terms of Hilbert schemes of lines, conics etc.
Finally, if time permits, I can say something about singular Fano 3-folds.