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Alexander Koldobsky has received his Ph.D. in 1982 from St Petersburg (Leningrad) State University. He is a Professor at the University of Missouri-Columbia since 1999. Author of 2 books and about 80 research articles in convex geometry, harmonic and functional analysis and probability. Over the years he developed a Fourier-analytic approach to multiple questions concerning volumes of sections and projections of convex bodies, allowing to solve a number of problems. A landmark achievement in this direction was the complete analytic solution of the 1956 Busemann-Petty Problem (Gardner, Koldobsky and Schlumprecht, Annals of Math. 1999). Other results of Koldobsky include a solution to the 1938 Schoenberg's problem on positive definite functions, stability results in volume comparison problems, complex intersection bodies and complex versions of the Busemann-Petty problem, estimates related to the hyperplane conjecture and its extensions to arbitrary measures instead of volume. His monograph ''Fourier analysis in convex geometry'' has according of MathSciNet about 130 citations. He was a visiting professor and researcher at several universities and mathematical institutes (Max Planck Institute-Bonn, Fields Institute, CRM, Weizmann Institute, Marne-la-Vall\'ee, Kiel, Warsaw, Toulouse). Koldobsky gave an impressive number of about 50 colloquium talks, several hundreds of seminar and conference talks. He was the main speaker at a CBMS conference. He supervised 7 postdocs and 7 Ph.D. students, organized several conferences and workshops related to the geometric functional analysis. |
