Abstract：I will report on some spectacular results obtained in the St. Petersburg school of Algebraic Groups, over the last few years. I would like to cover 1) the work by Ivan Panin and others on the Grothendieck---Serre problem, 2) the work by Anastasia Stavrova, Victor Petrov and Alexei Stepanov on the structure of isotropic reductive groups, 3) the work by Andrei Lavrenov and Sergei Sinchuk on centrality of K_2 and the K_2-analogue of Serre's conjecture, and 4) my own work, joint with Zuhong Zhang, on the relative reverse decomposition of unipotents, and commutator formulae. Time permitting, I could mention some other related topics.
