Russian Mathematical Surveys最新文献

{"title":"Tetrahedron equation: algebra, topology, and integrability","authors":"D. Talalaev","doi":"10.1070/RM10009","DOIUrl":"https://doi.org/10.1070/RM10009","url":null,"abstract":"The Zamolodchikov tetrahedron equation inherits almost all the richness of structures and topics in which the Yang–Baxter equation is involved. At the same time, this transition symbolizes the growth of the order of the problem, the step from the Yang–Baxter equation to the local Yang–Baxter equation, from the Lie algebra to the 2-Lie algebra, from ordinary knots in to 2-knots in . These transitions are followed in several examples, and there are also discussions of the manifestation of the tetrahedron equation in the long-standing question of integrability of the three-dimensional Ising model and a related model of neural network theory: the Hopfield model on a two-dimensional lattice. Bibliography: 82 titles.","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"3 1","pages":"685 - 721"},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59011948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Vladimir Igorevich Bogachev","authors":"Petr Anatol'evich Borodin, Il'dar Abdullovich Ibragimov, B. Kashin, Valery Vasil'evich Kozlov, Aleksandr Viktorovich Kolesnikov, S. V. Konyagin, E. D. Kosov, O. Smolyanov, N. A. Tolmachev, D. Treschev, Alexander Shaposhnikov, Stanislav Valer'evich Shaposhnikov, A. Shiryaev, A. Shkalikov","doi":"10.1070/RM9997","DOIUrl":"https://doi.org/10.1070/RM9997","url":null,"abstract":"The prominent mathematician Vladimir Igorevich Bogachev, Professor at the Department of the Theory of Functions and Functional Analysis of the Faculty of Mechanics and Mathematics at Lomonosov Moscow State University, Professor at the Faculty of Mathematics of the HSE University, and Professor at the Department of Mathematics of the Faculty of Informatics and Applied Mathematics at St Tikhon’s Orthodox University, celebrated his sixtieth birthday on 14 February 2021. He was born in Moscow. His parents worked for defence industry and were involved directly in launching Earth satellites and ballistic missiles. After graduating from Moscow secondary school no. 19 with a gold medal, where B. L. Geidman was his mathematics teacher, Bogachev enrolled at the Faculty of Mechanics and Mathematics at Moscow State University, and later started postgraduate studies there with O. G. Smolyanov as his scientific advisor. He completed his postgraduate studies ahead of time, and in 1986, after defending his PhD thesis, begun to work at the same Faculty. Bogachev is a major expert in measure theory, the theory of probability, infinitedimensional analysis, and partial differential equations. He has solved a number of difficult problems stated by well-known mathematicians, and has obtained fundamental results in the theory of Gaussian distributions, investigated the differentiability properties of measures, and developed a new line of research in the theory of Fokker–Planck–Kolmogorov equations. His first papers, published in the early 1980s, concerned measure theory in infinite-dimensional spaces and the theory of differentiable measures, where he continued the research of his advisor Smolyanov. Bogachev gained recognition by successfully solving three problems posed by Aronszajn in the theory of infinite-dimensional probability distributions. Aronszajn proposed the following definition as an infinite-dimensional analogue of a set with Lebesgue measure zero.","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"76 1","pages":"1149 - 1157"},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59006655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Vyacheslav Vladimirovich Shokurov","authors":"V. Alexeev, C. Birkar, F. Bogomolov, Y. Zarhin, V. Nikulin, Dmitri Orlov, A. N. P. Y. G. Prokhorov, M. Reid, A. Tikhomirov, I. Cheltsov","doi":"10.1070/RM10002","DOIUrl":"https://doi.org/10.1070/RM10002","url":null,"abstract":"On 18 May 2020, Vyacheslav Shokurov, a great scientist, leading researcher at the Steklov Mathematical Institute of the Russian Academy of Sciences, and Professor of Mathematics at the Johns Hopkins University in Baltimore, turned 70 years old. Vyacheslav Shokurov is a world-leading expert in birational algebraic geometry, who has completely reshaped this area of modern mathematics. His novel research, which often used amazing approaches, underlies many current trends in this area. The impact he has had on higher-dimensional birational geometry with his deep insight, new methods, and prophetic conjectures (many of them still open) cannot be overestimated. Vyacheslav Shokurov was born in Moscow. He was educated in High School no. 2, one of the best mathematical schools in Moscow at the time. Many former students of this school became famous scientists in their later lives. Among his mathematics teachers in the school were several faculty members of Moscow State University, and some students from this university were assisting. One of these","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"76 1","pages":"553 - 556"},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59011800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Convergence of Bieberbach polynomials: Keldysh’s theorems and Mergelyan’s conjecture","authors":"A. Aptekarev","doi":"10.1070/RM9991","DOIUrl":"https://doi.org/10.1070/RM9991","url":null,"abstract":"Results due to Keldysh on the convergence of Bieberbach polynomials and the density of polynomials in spaces of analytic functions are considered. Their further development and relevance in the contemporary context of constructive complex analysis are discussed. Particular focus is placed on Mergelyan’s conjecture on the rate of convergence in a domain with smooth boundary, which is still open. Bibliography: 20 titles.","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"76 1","pages":"379 - 387"},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59005731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Questions in algebra and mathematical logic. Scientific heritage of S. I. Adian","authors":"V. S. Atabekyan, L. Beklemishev, V. Guba, I. Lysenok, A. Razborov, A. L. Semenov","doi":"10.1070/RM9980","DOIUrl":"https://doi.org/10.1070/RM9980","url":null,"abstract":"This is a survey of results on the Burnside problem and properties of Burnside groups, the finite basis problem for group identities, periodic products of groups and Malcev’s problem, construction of groups with special properties (Tarski monsters), constructive bounds in the Burnside- Magnus problem, and algorithmic problems: the problem of recognition of group properties, the word problem for semigroups with one relation, and semi-Thue systems. The focus is on the most important results obtained in papers of Adian and his students. Bibliography: 81 titles.","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"38 1","pages":"1 - 27"},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59005444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sergei Ivanovich Adian","authors":"V. Atabekyan, L. Beklemishev, V. Buchstaber, S. Goncharov, V. Guba, Y. Ershov, V. Kozlov, I. Lysenok, S. Novikov, Y. Osipov, M. Pentus, V. Podolskii, A. Razborov, V. Sadovnichii, A. L. Semenov, A. Talambutsa, D. Treschev, L. N. Shevrin","doi":"10.1070/RM9989","DOIUrl":"https://doi.org/10.1070/RM9989","url":null,"abstract":"Academician Sergei Ivanovich Adian (1 January 1931 —5 May 2020), one of the most prominent Russian mathematicians, was born in the mountain village of Kushchi, in the Dashkasan district of the Azerbaijan Soviet Socialist Republic, which lies 40 kilometers away from the town of Ganja (which was soon renamed Kirovabad, but now is Ganja again). His father Ivan Arakelovich Adian was a carpenter, a son of a herdsman, and his mother Lusik was a daughter of Konstantin Truzyan, a peasant. Two years later Sergei Adian’s parents moved to Kirovabad. By the beginning of World War II they had four children. In 1941, during the first days of the war the father was conscripted and was soon killed when his unit was surrounded. Sergei, like his parents, did not speak Russian, but in 1938 they sent him to the Russian secondary school no. 11 in Kirovabad, where his mathematical abilities became obvious quite early. When he graduated, the public education department of Kirovabad applied to have him included in the Azerbaijan quota of graduates sent to study at Moscow State University. The application was declined (it was mainly ethnic Azerbaijanis that were accepted), and as a result he enrolled in","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"76 1","pages":"177 - 181"},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59005554","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multipoint formulae for inverse scattering at high energies","authors":"R. Novikov","doi":"10.1070/RM9994","DOIUrl":"https://doi.org/10.1070/RM9994","url":null,"abstract":"","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"76 1","pages":"723 - 725"},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59006044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Separation of variables for type [IMG align=ABSMIDDLE alt=$ D_n$]tex_rm_5265_img1[/IMG] Hitchin systems on hyperelliptic curves","authors":"P. I. Borisova","doi":"10.1070/RM9935","DOIUrl":"https://doi.org/10.1070/RM9935","url":null,"abstract":"","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"76 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59004916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Vasilii Mikhailovich Babich","authors":"M. Belishev, S. Dobrokhotov, I. Ibragimov, A. P. Kiselev, S. Kislyakov, M. Lyalinov, Y. Matiyasevich, V. Romanov, V. Smyshlyaev, T. Suslina, N. Ural'tseva","doi":"10.1070/RM9987","DOIUrl":"https://doi.org/10.1070/RM9987","url":null,"abstract":"On 13 June 2020 the prominent mathematician and expert in mechanics, head of the St. Petersburg school in the theory of diffraction and wave propagation Vasilii Mikhailovich Babich observed his 90th birthday. He is the author of many now classical results on the structure of high-frequency asymptotics of solutions of various problems in mathematical physics. The pioneering works in which he developed the ray method for elastic body and surface waves are particularly notable, as are his asymptotic constructions of localized solutions of linear partial differential equations, which have found many applications, and also a series of his papers justifying formulae for high-frequency asymptotics. Babich is an Honoured Scientist of the Russian Federation (2010). His achievements have been marked by the USSR State Prize, which he received together with A. S. Alekseev, V. S. Buldyrev, I. A. and L. A. Molotkov, G. I. Petrashen, and T.B. Yanovskaya for the development of the ray method (1982), the V.A. Fock prize of the Russian Academy of Sciences for the development of asymptotic methods in diffraction theory (1998), and the prize “A Life Devoted to Mathematics” of the Dynasty Foundation (2014). In previous issues of this journal there are tributes on the occasions of his 70th and 80th birthdays1 to Babich’s research, teaching, and organizational activities in science. A. P. Kiselev and V. P. Smyshlyaev analysed his role in the development of the St. Petersburg school of the theory of diffraction and wave propagation in the paper “The 70th birthday of V. M. Babich” (Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 275 (2001), 9–16).2 Babich continues to do fruitful research in mathematical physics; in particular, he works on the theory of complex interference waves [1], [2]. In recent years he","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"76 1","pages":"193 - 194"},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59005337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Interpolation properties of Hermite–Padé polynomials","authors":"S. Suetin","doi":"10.1070/RM10000","DOIUrl":"https://doi.org/10.1070/RM10000","url":null,"abstract":"where σ1 is a positive measure with support supp σ1 on a compact set E ⊂ R and h ∈ H (E) is a holomorphic function on E. If h(z) = σ̂2(z), where σ2 is a positive measure with support supp σ2 ⊂ F , where F ⊂ R E is a compact set, then the pair of functions f1, f2 forms a Nikishin system (see [6], and also [7], [5], [10], and the bibliography therein). Let Qn,j , j = 0, 1, 2, be the Hermite–Padé polynomials of the first type for the collection [1, f1, f2] with multi-index n = (n − 1, n, n), which means that deg Qn,j ⩽ n and (Qn,0 + Qn,1f1 + Qn,2f2)(z) = O(z−2n−2), z →∞. (2) For an arbitrary polynomial Q ∈ C[z] 0, let","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"76 1","pages":"543 - 545"},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59011762","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}