Work
Milman received his Ph.D. at Kharkov State University in 1965 under the direction of Boris Levin.
In a famous 1971 paper, Milman gave a new proof of Dvoretzky's theorem, stating that every convex body in dimension N has a section of dimension d(N), with d(N) tending to infinity with N, that is isomorphic to an ellipsoid. Milman's proof gives the optimal bound d(N) ≥ const log N. In this proof, Milman put forth the concentration of measure phenomenon which has since found numerous applications.
Milman made important contributions to the study of Banach spaces of large (finite) dimension, which led to the development of asymptotic geometric analysis. His results in this field include Milman's reverse Brunn–Minkowski inequality and the quotient of subspace theorem.
Read more about this topic: Vitali Milman
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