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Register a new userOn the 80th Birthday of Dmitry Borisovich Fuchs
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This article is a collection of several memories for a special issue of SIGMA devoted to Dmitry Borisovich Fuchs.
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Boris R. Vainberg was born on March 17, 1938, in Moscow. His father was a Lead Engineer in an aviation design institute. His mother was a homemaker. From early age, Boris was attracted to mathematics and spent much of his time at home and in school working through collections of practice problems for the Moscow Mathematical Olympiad. His first mathematical library consisted of the books he received as one of the prize-winners of these olympiads.
The article is a report on the biography and achievements of Ernest Borisovich Vinberg, an outstanding Russian mathematician, who passed away in Moscow on May 12, 2020. We discuss his contributions to various areas of mathematics such as Riemannian and Lobachevsky geometries, homogeneous convex cones, Lie groups and Invariant theory, equivariant symplectic geometry and Poisson structures.
The essay is devoted to the personality of the prominent theorist D.V. Volkov and his pioneer works in quantum field theory and elementary particle physics.
This paper describes the work of Jesse Douglas on the Plateau problem, work for which he was awarded a Fields Medal in 1936, and considers the contributions Tibor Rado made in the 1930s.
Like his colleagues de Prony, Petit, and Poisson at the Ecole Polytechnique, Cauchy used infinitesimals in the Leibniz-Euler tradition both in his research and teaching. Cauchy applied infinitesimals in an 1826 work in differential geometry where infinitesimals are used neither as variable quantities nor as sequences but rather as numbers. He also applied infinitesimals in an 1832 article on integral geometry, similarly as numbers. We explore these and other applications of Cauchys infinitesimals as used in his textbooks and research articles. An attentive reading of Cauchys work challenges received views on Cauchys role in the history of analysis and geometry. We demonstrate the viability of Cauchys infinitesimal techniques in fields as diverse as geometric probability, differential geometry, elasticity, Dirac delta functions, continuity and convergence. Keywords: Cauchy--Crofton formula; center of curvature; continuity; infinitesimals; integral geometry; limite; standard part; de Prony; Poisson
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