Krylov studied at Lomonosov University, where he in 1966 under E. B. Dynkin attained a doctoral candidate title (similar to a PhD) and in 1973 a Russian doctoral degree (somewhat more prestigious than a PhD).
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In the mathematical field of Lie theory, a Dynkin diagram, named for Eugene Dynkin, is a type of graph with some edges doubled or tripled (drawn as a double or triple line) and, within certain constraints, directed multiple edges.