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EMS Newsletter December 2016 31 doctoral thesis2 was also related to Piatetski-Shapiro’s question. It concerned the Selberg conjecture about arithmeticity of discrete subgroups, so-called lattices, in semisimple Lie groups. Piatetski-Shapiro was interested in this problem but he did not manage to solve it, although he had some results in this direction. I developed a theory of hyperbolic reflection groups, which permitted me to construct many counterexamples at rank one. After that, Margulis proved his famous theorem for higher rank, answering affirmatively the Selberg conjecture. My work on hyperbolic reflection groups had two sources: one was Dynkin’s theory of simple roots, which is tightly related to finite reflection groups; and the other was the theory of automorphic forms for lattices in semisimple Lie groups, which was a favourite subject of PiatetskiShapiro. So in a sense I continued studying some questions they posed to me (both Dynkin and PiatetskiShapiro). In 1966, there was the International Congress Discoveries, not Inventions – Interview with Ernest Borisovich Vinberg