Discoveries, not Inventions – Interview with Ernest Borisovich Vinberg

摘要

In fact, I had two advisors: Evgeny Borisovich Dynkin and Ilya Iosifovich Piatetski-Shapiro. They were both distinguished mathematicians. Dynkin was a brilliant lecturer, attracting a lot of young people, but Piatetski-Shapiro posed the problem which was kind of a challenge. This problem concerned homogeneous bounded domains. The question posed by élie Cartan was whether any such domain is symmetric, and Piatetski-Shapiro gave a counterexample in dimension 4. Then a problem arose to give a classification of homogeneous bounded domains in complex spaces. And this turned out to be related to classification of homogeneous convex cones in real vector spaces, which was the subject of my PhD thesis.