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.

On 27 February 2014 Professor Vladimir Fedorovich Molchanov, Doctor of the Physical and Mathematical Sciences, observed his 75th birthday. He is a specialist in representation theory and non-commutative harmonic analysis, the author of 48 research papers and a contributor, together with N.Ya. Vilenkin and A.U. Klimyk, to the volume Representation theory and non-commutative harmonic analysis II (Encyclopaedia Math. Sci., 59) [1]. Vladimir Fedorovich was born in 1939 in Krasnoyarsk. His family moved to Tambov in the fall of 1945, after the demobilization of his father, an officer in the Soviet Army. After finishing Tambov secondary school no. 1 with a gold medal in 1955, he enrolled in the Faculty of Mechanics and Mathematics of Moscow State University, followed by postgraduate studies there under the guidance of F. A. Berezin. Since 1965 he has worked in the Department of Mathematical Analysis (as its head since 1966) of Tambov State Pedagogical Institute (now G. R. Derzhavin Tambov State University). We briefly discuss his best-known results.

On 2 July 2009 the prominent mathematician Mikhail Shlemovich Birman, a leading authority on the spectral theory of operators, passed away. He was born on 17 January 1928 in Leningrad. His father was a researcher specializing in theoretical mechanics and a professor, and his mother was a schoolteacher. Birman studied in the Faculty of Mathematics and Mechanics at the Leningrad State University in 1946–1950, specializing in computational methods. As his principal teachers he viewed M. K. Gavurin, who supervised his diploma thesis, and L. V. Kantorovich. Already as a student, Birman took a part-time job at the Leningrad Branch of the Mathematical Institute, in the laboratory headed by Kantorovich. He was the best student of his year, distinguished by a high intellectual level and independent ways of thinking. However, he was not admitted to postgraduate study because of the anti-Semitic policies of that time. In 1947 Birman married the same-year student Tat’yana Petrovna Il’ina. In 1948 their son Zhenya was born. The happy marriage with Tat’yana lasted all his life. She died two years before him. She was always his guardian angel, and it is thanks to her love and care that he could fully devote himself to his favourite activity, the study of mathematics. Upon graduating from the university Birman taught as an assistant professor in the Department of Higher Mathematics of the Leningrad Mining Institute. In 1954 he successfully defended his Ph.D. dissertation. An important factor in the formation of Birman as a researcher was his active participation in the Leningrad seminar on mathematical physics, which was organized in the early 1950s on the initiative of V. I. Smirnov. Subsequently Birman and O. A. Ladyzhenskaya supervised this seminar for many years. Following a proposal of Smirnov and Ladyzhenskaya, Birman moved in 1956 to the Leningrad State University, in the Department of Mathematical Physics of the Faculty of Physics. There he worked for more than 50 years, until the end

The outstanding mathematician Mark Iosifovich Graev celebrated his 85th birthday on 21 November 2007. For many years he has been one of the most authoritative and recognized experts in the area of representation theory and its applications, and the principal co-author of one of the founders of modern representation theory, I. M. Gel’fand. Mark’s father was born and grew up in a large and poor family in the city of Slutsk, finished gymnasium with a gold medal before the First World War, and entered the Faculty of Mathematics of Petrograd University. However, because of the well-known events of those years, he was forced to interrupt his studies. Until the mid-1930s, the father was a political worker in the Red Army, and after being discharged from the army he worked as a teacher. The military establishment where he worked (it was located at the precise spot of the present Peoples’ Friendship University), patronized the Moscow Art Theater, and this allowed young Mark to watch almost all performances in the theater many times. Before the beginning of the war, Mark’s mother was in charge of the school library. His father was able to cultivate in Mark the idea of mathematics as a powerful science that gives answers to all of life’s questions. In 1930 Mark was accepted directly into the second grade of school. A young mathematics teacher stimulated his study of and passion for mathematics in the early years. She was able to recognize the talent of her pupil and fill him with confidence in his abilities. Starting in 1937, he attended a school study group at Moscow State University (MSU) and he still remembers the awe with which he crossed the threshold of the building at Mokhovaya Street. In 1939 he received first prize in the Mathematical Olympiad at the university, and together with a letter of commendation he also got a stack of books, among them P. S. Aleksandrov’s book on group theory with the author’s autograph, mathematical works of Newton, and others.

Vladimir Gilelevich Maz’ya, the prominent mathematician and author of numerous publications and fundamental results in various fields of analysis and mathematical physics, celebrated his 70th birthday on 31 December 2007. V. G. Maz’ya was born in Leningrad in 1937. His father was killed at the front in 1941, and both his grandfathers and grandmothers died during the siege of Leningrad. His mother raised Vladimir all by herself. The two lived together on her meagre salary of an accountant, sharing a nine-square-meter room in a large communal flat. Vladimir finished secondary school with a gold medal, and in his last school years he was a repeated winner of city olympiads in mathematics and physics. In 1955 Maz’ya entered the Faculty of Mathematics and Mechanics of Leningrad State University (LSU). His first papers were published quite early: the first (on the Dirichlet problem for second-order elliptic equations) appeared in Doklady Akad. Nauk SSSR in 1959 when he was a fourth-year student. In the same year he gave two talks at the seminar of V. I. Smirnov, on necessary and sufficient conditions for the validity of integral inequalities of Sobolev type. The results were published in Doklady in 1960. For this work he became the first winner of the Prize for Young Mathematicians, established in 1962 by the Leningrad Mathematical Society. After graduating from the university, Maz’ya obtained a position of junior research fellow at the Research Institute of Mathematics and Mechanics of LSU. In 1961 he organized a mathematical school for high school students at the Faculty of Mathematics and Mechanics and became its first director. He defended his Ph.D. thesis entitled “Classes of sets and embedding theorems for function spaces” in 1962 at Moscow State University. It was based on ideas from his talks at Smirnov’s seminar. In their reviews, the opponents and the external reviewer noted that the level of the work far exceeded the requirements of the Higher Certification Commission for Ph.D. theses, and his work was recognized as outstanding at the thesis defence in the Academic Council of Moscow State University. Maz’ya had no formal research advisor either for his master’s thesis or for his Ph.D. thesis: he himself chose his research topics, and he solved the problems by

On 26 April 2007 Leonid Romanovich Volevich passed away after a severe illness. He was born in Moscow on 11 July 1934. His father was a well-known neuropathologist, and his mother was a translator and teacher of foreign literature. In 1952 he entered the Faculty of Mechanics and Mathematics of Moscow State University, where in his fourth year he began participating in O. A. Oleinik’s seminar. In 1957 he graduated and became a Ph.D. student of K. I. Babenko in the Division of Applied Mathematics of the Steklov Mathematical Institute. In 1960 he defended his Ph.D. thesis “Local properties of solutions of systems of partial differential equations” and stayed to work in the department led by Babenko at the Institute of Applied Mathematics organized by M. V. Keldysh. There he worked his whole life, in the position of principal researcher from 1997. In 1971 he defended his D.Sc. thesis “Investigations of non-homogeneous pseudodifferential operators (regularity of solutions and the Cauchy problem)”. Volevich was a permanent and active participant in M. I. Vishik’s university seminar from its very beginning. In 1965 the Executive Committee of the Moscow Mathematical Society appointed Oleinik as editor of the journal Trudy Moskovskogo Matematicheskogo Obshchestva (translated as Transactions of the Moscow Mathematical Society) and Volevich as deputy editor. After Oleinik’s death he became the editor of the journal by the decision of the Executive Committee. Fifty-three volumes of the journal were published with his direct assistance. He was also a member of the editorial board of the journal Mathematische Nachrichten. Volevich contributed greatly to the general theory of partial differential equations. The foundations of this theory, which goes back to investigations of the classical mathematicians of the 18th and 19th centuries, were laid by J. Hadamard, S. N. Bernstein, I. G. Petrovskii, J. Leray, and S. L. Sobolev. The theory was later further developed and extended in work of Vishik, O. A. Ladyzhenskaya, L. Nirenberg, Oleinik, L. Hörmander, and others.

This is an expanded version of a lecture given in Vienna on January 17, 1990 in which the significance of a famous paper by Radon, and the developments originating from it, were discussed.

The Penrose twistor theory is very close to integral geometry in the sense of Gelfand both in the way it states its problems and in the way it uses its technical means. Actually, one can consider the Penrose transform as an analogue of the Radon-John transform for ∂-cohomologies. However, there are other common points, and their close scrutiny is very instructive for both theories. For example, the study of curved twistor manifolds [1] is very similar to integral geometry of the manifold of curves [2 – 4]. In this paper we present a review of several such «boundaryå questions. All consideration are made over C.

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