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Proceedings of the International Congress of Mathematicians (ICM 2018)最新文献

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HIGHER ORDER COMMUTATORS AND MULTI-PARAMETER BMO 高阶换向器和多参数bmo
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0115
S. Petermichl
{"title":"HIGHER ORDER COMMUTATORS AND MULTI-PARAMETER BMO","authors":"S. Petermichl","doi":"10.1142/9789813272880_0115","DOIUrl":"https://doi.org/10.1142/9789813272880_0115","url":null,"abstract":"In this article we highlight the interplay ofmulti-parameter BMO spaces and boundedness of corresponding commutators. In a variety of settings, we discuss two-sided norm estimates for commutators of classical singular operators with a symbol function. In its classical form, this concerns a theorem by Nehari, factorisation of Hardy space, Hankel and Toeplitz forms. We highlight recent results in which a characterization of Lp boundedness of iterated commutators of multiplication by a symbol function and tensor products of Riesz and Hilbert transforms is obtained, completing a theory on characterisation of BMO spaces begun by Cotlar, Ferguson and Sadosky. In the light of real analysis, we discuss results in a more intricate situation; commutators of multiplication by a symbol function and Calderón-Zygmund or Journé operators. We show that the boundedness of these commutators is also determined by the inclusion of their symbol function in the same multi-parameter BMO class. In this sense the Hilbert or Riesz transforms or their tensor products are a representative testing class for Calderón-Zygmund or Journé operators.","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"107 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132160360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
SUBADDITIVE COCYCLES AND HOROFUNCTIONS 次加性环与函数
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0124
S. Gouëzel
{"title":"SUBADDITIVE COCYCLES AND HOROFUNCTIONS","authors":"S. Gouëzel","doi":"10.1142/9789813272880_0124","DOIUrl":"https://doi.org/10.1142/9789813272880_0124","url":null,"abstract":"Subadditive cocycles are the random version of subadditive sequences. They play an important role in probability and ergodic theory, notably through Kingman’s theorem ensuring their almost sure convergence. We discuss a variation around Kingman’s theorem, showing that a subadditive cocycle is in fact almost additive at many times. This result is motivated by the study of the iterates of deterministic or random semicontractions on metric spaces, and implies the almost sure existence of a horofunction determining the behavior at infinity of such a sequence. In turn, convergence at infinity follows when the geometry of the space has some features of nonpositive curvature. The aim of this text is to present and put in perspective the results we have proved with Anders Karlsson in the article Gouëzel and Karlsson [2015]. The topic of this article is the study, in an ergodic theoretic context, of some subadditivity properties, and their relationships with dynamical questions with a more geometric flavor, dealing with the asymptotic behavior of random semicontractions on general metric spaces. This text is translated from an article written in French on the occasion of the first congress of the French Mathematical Society Gouëzel, Sébastien [2017]. The proof of the main ergodic-theoretic result in Gouëzel and Karlsson [2015] has been completely formalized and checked in the computer proof assistant Isabelle/HOL Gouëzel, Sébastien [2016]. 1 Iteration of a semicontraction on Euclidean space In order to explain the problems we want to consider, it is enlightening to start with a more elementary example, showing how subadditivity techniques can be useful to understand a deterministic semicontraction. In the next section, we will see how these results can be extended to random semicontractions. MSC2010: primary 37H15; secondary 37A30.","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129495090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
ON THE CONVERGENCE OF NUMERICAL SCHEMES FOR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS 守恒双曲型系统数值格式的收敛性
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0195
Siddhartha Mishra
{"title":"ON THE CONVERGENCE OF NUMERICAL SCHEMES FOR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS","authors":"Siddhartha Mishra","doi":"10.1142/9789813272880_0195","DOIUrl":"https://doi.org/10.1142/9789813272880_0195","url":null,"abstract":"A large variety of efficient numerical methods, of the finite volume, finite difference and DG type, have been developed for approximating hyperbolic systems of conservation laws. However, very few rigorous convergence results for these methods are available. We survey the state of the art on this crucial question of numerical analysis by summarizing classical results of convergence to entropy solutions for scalar conservation laws. Very recent results on convergence of ensemble Monte Carlo methods to the measure-valued and statistical solutions of multi-dimensional systems of conservation laws are also presented.","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"194 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131336993","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
LONG-TERM HISTORY AND EPHEMERAL CONFIGURATIONS 长期的历史和短暂的配置
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0021
C. Goldstein
{"title":"LONG-TERM HISTORY AND EPHEMERAL CONFIGURATIONS","authors":"C. Goldstein","doi":"10.1142/9789813272880_0021","DOIUrl":"https://doi.org/10.1142/9789813272880_0021","url":null,"abstract":"Mathematical concepts and results have often been given a long history, stretching far back in time. Yet recent work in the history of mathematics has tended to focus on local topics, over a short term-scale, and on the study of ephemeral configurations of mathematicians, theorems or practices. The first part of the paper explains why this change has taken place: a renewed interest in the connections between mathematics and society, an increased attention to the variety of components and aspects of mathematical work, and a critical outlook on historiography itself. The problems of a long-term history are illustrated and tested using a number of episodes in the nineteenth-century history of Hermitian forms, and finally, some open questions are proposed.","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"85 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131357372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
PROOF-THEORETIC METHODS IN NONLINEAR ANALYSIS 非线性分析中的证明理论方法
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0045
U. Kohlenbach
{"title":"PROOF-THEORETIC METHODS IN NONLINEAR ANALYSIS","authors":"U. Kohlenbach","doi":"10.1142/9789813272880_0045","DOIUrl":"https://doi.org/10.1142/9789813272880_0045","url":null,"abstract":"We discuss applications of methods from proof theory, so-called proof interpretations, for the extraction of explicit bounds in convex optimization, fixed point theory, ergodic theory and nonlinear semigroup theory. Mathematics Subject Classification (2010): Primary 03F10; Secondary 03F35, 47H10, 47H20, 47H25, 90C30.","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123465000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 49
THE WORK OF PETER SCHOLZE Peter scholze的作品
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0004
M. Rapoport
{"title":"THE WORK OF PETER SCHOLZE","authors":"M. Rapoport","doi":"10.1142/9789813272880_0004","DOIUrl":"https://doi.org/10.1142/9789813272880_0004","url":null,"abstract":"This is my laudation for Scholze's Fields medal 2018.","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121512771","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
SHARP SPHERE PACKINGS 尖球填料
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0063
M. Viazovska
{"title":"SHARP SPHERE PACKINGS","authors":"M. Viazovska","doi":"10.1142/9789813272880_0063","DOIUrl":"https://doi.org/10.1142/9789813272880_0063","url":null,"abstract":"The classical sphere packing problem asks for the densest possible configuration of nonoverlapping equal balls in the three dimensional Euclidean space. This natural and even naive question remained open for several centuries and has driven a lot of research in geometry, combinatorics and optimization. The complete proof of the sphere packing problem was given by T. Hales in 1998 Hales [2005]. A similar question can be asked for Euclidean spaces of dimensions other then three or for spaces with other geometries, such as a sphere, a projective space, or the Hamming space. The packing problem is not only an exiting mathematical puzzle, it also plays a role in computer science and signal processing as a mathematical model of the error correcting codes. In this paper we will focus on the upper bounds for the sphere packing densities. There exist different methods for proving such bounds. One conceptually simple and still rather powerful approach is the linear programming. We are particularly interested in those packing problems, which can be completely solved by this method. We will call such arrangements of balls the sharp packings. The sharp packings have many interesting properties. In particular, the distribution of pairwise distances between the centers of sharply packed spheres gives rise to summation and interpolation formulas. In the last section of this paper we will discuss a new interpolation formula for the Schwartz functions on the real line.","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124626493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
FRONT MATTER 前页
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_fmatter02
B. Sirakov, Paulo Ney de Souza, M. Viana
{"title":"FRONT MATTER","authors":"B. Sirakov, Paulo Ney de Souza, M. Viana","doi":"10.1142/9789813272880_fmatter02","DOIUrl":"https://doi.org/10.1142/9789813272880_fmatter02","url":null,"abstract":"","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121710241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
MACHINE-ASSISTED PROOFS MACHINE-ASSISTED证明
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0038
J. Davenport, B. Poonen, J. Maynard, H. Helfgott, P. Tiep, L. Cruz-Filipe
{"title":"MACHINE-ASSISTED PROOFS","authors":"J. Davenport, B. Poonen, J. Maynard, H. Helfgott, P. Tiep, L. Cruz-Filipe","doi":"10.1142/9789813272880_0038","DOIUrl":"https://doi.org/10.1142/9789813272880_0038","url":null,"abstract":"","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131097065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
ALI NESIN AND THE NESIN MATHEMATICS VILLAGE 阿里·奈辛和奈辛数学村
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0002
G. Greuel
{"title":"ALI NESIN AND THE NESIN MATHEMATICS VILLAGE","authors":"G. Greuel","doi":"10.1142/9789813272880_0002","DOIUrl":"https://doi.org/10.1142/9789813272880_0002","url":null,"abstract":"","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127072893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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