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

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NUMERICAL MATHEMATICS OF QUASICRYSTALS 准晶体的数值数学
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0193
Kai Jiang, Pingwen Zhang
{"title":"NUMERICAL MATHEMATICS OF QUASICRYSTALS","authors":"Kai Jiang, Pingwen Zhang","doi":"10.1142/9789813272880_0193","DOIUrl":"https://doi.org/10.1142/9789813272880_0193","url":null,"abstract":"Quasicrystals are one kind of fascinating aperiodic structures, and give a strong impact on material science, solid state chemistry, condensed matter physics and soft matters. The theory of quasicrystals, included in aperiodic order, has grown rapidly in mathematical and physical areas over the past few decades. Many scientific problems have been explored with the efforts of physicists and mathematicians. However, there are still lots of open problems which might to be solved by the close collaboration of physicists, mathematicians and computational mathematicians. In this article, we would like to bridge the physical quasicrystals and mathematical quasicrystals from the perspective of numerical mathematics.","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"39 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":"127269721","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: 7
BOUNDARY DYNAMICS FOR SURFACE HOMEOMORPHISMS 曲面同胚的边界动力学
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0127
Andres Koropecki, M. Nassiri
{"title":"BOUNDARY DYNAMICS FOR SURFACE HOMEOMORPHISMS","authors":"Andres Koropecki, M. Nassiri","doi":"10.1142/9789813272880_0127","DOIUrl":"https://doi.org/10.1142/9789813272880_0127","url":null,"abstract":"We discuss some aspects of the topological dynamics of surface homeomorphisms. In particular, we survey recent results about the dynamics on the boundary of invariant domains, its relationship with the induced dynamics in the prime ends compactification, and its applications in the area-preserving setting following our recent works","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"71 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":"121815858","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
ALGEBRAIC SURFACES WITH MINIMAL BETTI NUMBERS 最小贝提数代数曲面
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0074
J. Keum
{"title":"ALGEBRAIC SURFACES WITH MINIMAL BETTI NUMBERS","authors":"J. Keum","doi":"10.1142/9789813272880_0074","DOIUrl":"https://doi.org/10.1142/9789813272880_0074","url":null,"abstract":"These are algebraic surfaces with the Betti numbers of the complex projective plane, and are called Q-homology projective planes. Fake projective planes and the complex projective plane are smooth examples. We describe recent progress in the study of such surfaces, singular ones and fake projective planes. We also discuss open questions. 1 Q-homology Projective Planes and Montgomery-Yang problem A normal projective surface with the Betti numbers of the complex projective plane CP 2 is called a rational homology projective plane or a Q-homology CP . When a normal projective surface S has only rational singularities, S is a Q-homology CP 2 if its second Betti number b2(S) = 1. This can be seen easily by considering the Albanese fibration on a resolution of S . It is known that a Q-homology CP 2 with quotient singularities (and no worse singularities) has at most 5 singular points (cf. Hwang and Keum [2011b, Corollary 3.4]). The Q-homology projective planes with 5 quotient singularities were classified in Hwang and Keum [ibid.]. In this section we summarize progress on the Algebraic Montgomery-Yang problem, which was formulated by J. Kollár. Conjecture 1.1 (Algebraic Montgomery–Yang Problem Kollár [2008]). Let S be a Qhomology projective plane with quotient singularities. Assume that S := SnSing(S) is simply connected. Then S has at most 3 singular points. This is the algebraic version ofMontgomery–Yang ProblemFintushel and Stern [1987], which was originated from pseudofree circle group actions on higher dimensional sphere. MSC2010: primary 14J29; secondary 14F05, 14J17, 14J26, 32Q40, 32N15.","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"175 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":"116534244","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
IN SEARCH OF THE SOURCES OF INCOMPLETENESS 寻找不完整的根源
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0212
J. Plato
{"title":"IN SEARCH OF THE SOURCES OF INCOMPLETENESS","authors":"J. Plato","doi":"10.1142/9789813272880_0212","DOIUrl":"https://doi.org/10.1142/9789813272880_0212","url":null,"abstract":"","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"3 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":"126019573","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: 4
ALESSIO FIGALLI: HIS CONTRIBUTIONS TO GEOMETRY AND ANALYSIS 阿莱西奥·菲加利:他对几何和分析的贡献
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0001
L. Caffarelli
{"title":"ALESSIO FIGALLI: HIS CONTRIBUTIONS TO GEOMETRY AND ANALYSIS","authors":"L. Caffarelli","doi":"10.1142/9789813272880_0001","DOIUrl":"https://doi.org/10.1142/9789813272880_0001","url":null,"abstract":"","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"28 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":"128756818","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: 1
FROM CONTINUOUS RATIONAL TO REGULOUS FUNCTIONS 从连续有理函数到正则函数
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0075
W. Kucharz, K. Kurdyka
{"title":"FROM CONTINUOUS RATIONAL TO REGULOUS FUNCTIONS","authors":"W. Kucharz, K. Kurdyka","doi":"10.1142/9789813272880_0075","DOIUrl":"https://doi.org/10.1142/9789813272880_0075","url":null,"abstract":"Let X be an algebraic set in Rn. Real-valued functions, defined on subsets of X , that are continuous and admit a rational representation have some remarkable properties and applications. We discuss recently obtained results on such functions, against the backdrop of previously developed theories of arc-symmetric sets, arc-analytic functions, approximation by regular maps, and algebraic vector bundles.","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"44 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":"131451010","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: 18
AN INTRODUCTION TO MULTILEVEL MONTE CARLO METHODS 介绍多层蒙特卡罗方法
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0192
M. Giles
{"title":"AN INTRODUCTION TO MULTILEVEL MONTE CARLO METHODS","authors":"M. Giles","doi":"10.1142/9789813272880_0192","DOIUrl":"https://doi.org/10.1142/9789813272880_0192","url":null,"abstract":"In recent years there has been very substantial growth in stochastic modelling in many application areas, and this has led to much greater use of Monte Carlo methods to estimate expected values of output quantities from stochastic simulation. However, such calculations can be expensive when the cost of individual stochastic simulations is very high. Multilevel Monte Carlo greatly reduces the computational cost by performing most simulations with low accuracy at a correspondingly low cost, with relatively few being performed at high accuracy and a high cost. This article reviews the key ideas behind the multilevel Monte Carlo method. Some applications are discussed to illustrate the flexibility and generality of the approach, and the challenges in its numerical analysis.","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"4 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":"132469693","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
DECOUPLINGS AND APPLICATIONS 解耦和应用
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0107
C. Demeter
{"title":"DECOUPLINGS AND APPLICATIONS","authors":"C. Demeter","doi":"10.1142/9789813272880_0107","DOIUrl":"https://doi.org/10.1142/9789813272880_0107","url":null,"abstract":"Abstract I will explain a few Fourier analytic results in the spirit of the Littlewood-Paley theorem, when curvature replaces lacunarity. I will explore a wide range of consequences in number theory (exponential sums, Diophantine inequalities, the Lindelof hypothesis) and PDEs (local smoothing for the wave equation, Strichartz estimates on the torus). This talk is purely expository, no proofs, intended for a general audience. Joint with Jean Bourgain.","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"115 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":"132704921","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: 4
DIMENSION THEORY OF SELF-SIMILAR SETS AND MEASURES 自相似集与测度的维数理论
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0125
M. Hochman
{"title":"DIMENSION THEORY OF SELF-SIMILAR SETS AND MEASURES","authors":"M. Hochman","doi":"10.1142/9789813272880_0125","DOIUrl":"https://doi.org/10.1142/9789813272880_0125","url":null,"abstract":"We report on recent results about the dimension and smoothness properties of selfsimilar sets and measures. Closely related to these are results on the linear projections of such sets, and dually, their intersections with affine subspaces. We also discuss recent progress on the the Bernoulli convolutions problem.","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"38 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":"128371254","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: 24
FRONT MATTER 前页
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_fmatter01
B. Sirakov, Paulo Ney de Souza, M. Viana
{"title":"FRONT MATTER","authors":"B. Sirakov, Paulo Ney de Souza, M. Viana","doi":"10.1142/9789813272880_fmatter01","DOIUrl":"https://doi.org/10.1142/9789813272880_fmatter01","url":null,"abstract":"","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"33 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":"132965268","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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