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
{"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":null,"pages":null},"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":null,"pages":null},"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":"Chaplygin ball in a solenoidal field","authors":"A. Borisov, A. Tsiganov","doi":"10.1070/RM9930","DOIUrl":"https://doi.org/10.1070/RM9930","url":null,"abstract":"According to Dirac, changes in the equations of motion related to additional external forces performing no work can be described in terms of deformations of the Poisson bracket. It is natural to ask whether or not Dirac’s ideas are valid in non-holonomic mechanics. We discuss this question here by taking the Chaplygin ball as an example. We consider the linear Lie–Poisson bracket on the Lie algebra e∗(3):","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59004771","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":"Landau–Ginzburg models of complete intersections in Lagrangian Grassmannians","authors":"V. Przyjalkowski, K. Rietsch","doi":"10.1070/RM9984","DOIUrl":"https://doi.org/10.1070/RM9984","url":null,"abstract":"Let LG(n) be the Lagrangian Grassmannian parameterizing the Lagrangian linear subspaces of the 2n-dimensional complex symplectic vector space. It has a Plücker embedding to a projective space P, so that for H = OP(1) we have Pic(LG(n)) = ZH. Let X ⊂ LG(n) be a smooth Fano complete intersection of degrees d1, . . . , dk. We have ∑k i=1 di < n + 1, and dk+1 = n + 1 − ∑k i=1 di is the Fano index of X. Let pi, i = 1, . . . , n, be formal variables. Consider the series","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59005263","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}
M. Belishev, S. Dobrokhotov, I. Ibragimov, A. P. Kiselev, S. Kislyakov, M. Lyalinov, Y. Matiyasevich, V. Romanov, V. Smyshlyaev, T. Suslina, N. Ural'tseva
{"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":null,"pages":null},"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":null,"pages":null},"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}
{"title":"Integrable polynomial Hamiltonian systems and symmetric powers of plane algebraic curves","authors":"V. Buchstaber, A. Mikhailov","doi":"10.1070/RM10007","DOIUrl":"https://doi.org/10.1070/RM10007","url":null,"abstract":"This survey is devoted to integrable polynomial Hamiltonian systems associated with symmetric powers of plane algebraic curves. We focus our attention on the relations (discovered by the authors) between the Stäckel systems, Novikov’s equations for the th stationary Korteweg– de Vries hierarchy, the Dubrovin–Novikov coordinates on the universal bundle of Jacobians of hyperelliptic curves, and new systems obtained by considering the symmetric powers of curves when the power is not equal to the genus of the curve. Bibliography: 52 titles.","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59011815","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}
Andryi Valer'evich Malyutin, E. Fominykh, E. Shumakova
{"title":"[IMG align=ABSMIDDLE alt=$ 3$]tex_rm_5298_img1[/IMG]-manifolds given by [IMG align=ABSMIDDLE alt=$ 4$]tex_rm_5298_img2[/IMG]-regular graphs with three Euler cycles","authors":"Andryi Valer'evich Malyutin, E. Fominykh, E. Shumakova","doi":"10.1070/rm10013","DOIUrl":"https://doi.org/10.1070/rm10013","url":null,"abstract":"","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59012253","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}
Boris Yakovlevich Kazarnovskii, A. Khovanskii, A. Esterov
{"title":"Newton polytopes and tropical geometry","authors":"Boris Yakovlevich Kazarnovskii, A. Khovanskii, A. Esterov","doi":"10.1070/RM9937","DOIUrl":"https://doi.org/10.1070/RM9937","url":null,"abstract":"The practice of bringing together the concepts of ‘Newton polytopes’, ‘toric varieties’, ‘tropical geometry’, and ‘Gröbner bases’ has led to the formation of stable and mutually beneficial connections between algebraic geometry and convex geometry. This survey is devoted to the current state of the area of mathematics that describes the interaction and applications of these concepts. Bibliography: 68 titles.","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59005162","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":"Equivariant minimal model program","authors":"Yuri Prokhorov","doi":"10.1070/RM9990","DOIUrl":"https://doi.org/10.1070/RM9990","url":null,"abstract":"The purpose of the survey is to systematize a vast amount of information about the minimal model program for varieties with group actions. We discuss the basic methods of the theory and give sketches of the proofs of some principal results. Bibliography: 243 titles.","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59005611","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}