Proceedings of the International Congress of Mathematicians (ICM 2018)最新文献_第2页

IMPA’S COMING OF AGE IN A CONTEXT OF INTERNATIONAL RECONFIGURATION OF MATHEMATICS 印帕在国际数学重构背景下的成长

Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0213

Tatiana Roque

{"title":"IMPA’S COMING OF AGE IN A CONTEXT OF INTERNATIONAL RECONFIGURATION OF MATHEMATICS","authors":"Tatiana Roque","doi":"10.1142/9789813272880_0213","DOIUrl":"https://doi.org/10.1142/9789813272880_0213","url":null,"abstract":"In the middle of the 20th century, the intimate link between science, industry and the state was stimulated, in its technical-scientific dimension, by the Cold War. Questions of a similar strategic nature were involved in the Brazilian political scene, when the CNPq was created. This presentation investigates the nature of the connection between this scientific policy and the presumed need for an advanced research institute in mathematics, that gave birth to IMPA. By retracing the scientific choices of the few mathematicians working at the institute in its first twenty years, we demonstrate how they paralleled the ongoing reconfiguration of scientific research. The development of dynamical systems theory provides a telling example of internationalization strategies which situated IMPA within a research network full of resources, that furnished, moreover, a modernizing drive adapted to the air of that time. On October 19, 1952, O Jornal do Comércio, a newspaper published in Brazil’s then capital city of Rio de Janeiro, reported that the National Research Council (CNP, Conselho Nacional de Pesquisas) had created an associated research arm called the Institute for Pure and AppliedMathematics (IMPA, Instituto deMatemática Pura e Aplicada). The National Research Council, later known as CNPq, had been created just a year beforehand and was directly connected to the country’s government. On the same day, the first pages of the newspaper reported: • The Soviet delegate presented a proposal for peace at the General Assembly of the United Nations. Stalin’s Foreign Minister, Andrei Vyshinsky called for a reduction of one-third of the armaments of the great powers and an unconditional ban on atomic weapons. The “peace pact” would be a condition to stop the then ongoing Korean War;","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":"132181607","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

INTERNATIONAL MATHEMATICAL KNOWLEDGE TRUST IMKT: AN UPDATE ON THE GLOBAL DIGITAL MATHEMATICS LIBRARY 国际数学知识信任imkt:全球数字数学图书馆的更新

Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0041

P. Ion, Thierry Bouche, G. Misra, A. Onshuus, S. Watt, Liu Zheng

引用次数: 0

REPRESENTATIONS OF FINITE GROUPS AND APPLICATIONS 有限群的表示及其应用

Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0052

P. Tiep

引用次数: 1

LOWER BOUNDS FOR SUBGRAPH ISOMORPHISM 子图同构的下界

Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0187

Benjamin Rossman

{"title":"LOWER BOUNDS FOR SUBGRAPH ISOMORPHISM","authors":"Benjamin Rossman","doi":"10.1142/9789813272880_0187","DOIUrl":"https://doi.org/10.1142/9789813272880_0187","url":null,"abstract":"We consider the problem of determining whether an Erdős–Rényi random graph contains a subgraph isomorphic to a fixed pattern, such as a clique or cycle of constant size. The computational complexity of this problem is tied to fundamental open questions including P vs. NP and NC1 vs. L. We give an overview of unconditional average-case lower bounds for this problem (and its colored variant) in a few important restricted classes of Boolean circuits. 1 Background and preliminaries The subgraph isomorphism problem is the computational task of determining whether a “host” graph H contains a subgraph isomorphic to a “pattern” graph G. When both G and H are given as input, this is a classic NP-complete problem which generalizes both the and H problems Karp [1972]. We refer to the Gsubgraph isomorphism problem in the setting where the pattern G is fixed and H alone is given as input. As special cases, this includes the kand kproblems when G is a complete graph or cycle of order k. For patterns G of order k, the G-subgraph isomorphism problem is solvable in time O(n) by the obvious exhaustive search.1 This upper bound can be improved toO(n) using any O(n) time algorithm for fast matrix multiplication Nešetřil and Poljak [1985] (the current record has ̨ < 2:38 Le Gall [2014]). Additional upper bounds are tied to structural parameters of G, such as an O(n) time algorithm for patterns G of treewidth w Plehn and Voigt [1990]. (See Marx and Pilipczuk [2014] for a survey on upper bounds.) The author’s work is supported by NSERC and a Sloan Research Fellowship. MSC2010: primary 68Q17; secondary 05C60. 1Throughout this article, asymptotic notation (O( ), Ω( ), etc.), whenever bounding a function of n, hides constants that may depend on G.","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"9 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":"114282894","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

HARMONIC MEASURE: ALGORITHMS AND APPLICATIONS 谐波测量:算法与应用

Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0106

C. Bishop

引用次数: 2

ANALYTIC TOOLS FOR THE STUDY OF FLOWS AND INVERSE PROBLEMS 研究流动和反问题的分析工具

Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0141

C. Guillarmou

引用次数: 0

CHARACTERISTIC SUBSETS AND THE POLYNOMIAL METHOD 特征子集与多项式方法

Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0064

M. N. Walsh

引用次数: 4

DEGENERATIONS AND MODULI SPACES IN KÄHLER GEOMETRY kÄhler几何中的退化和模空间

Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0085

Song Sun

引用次数: 5

NONHYPERBOLIC ERGODIC MEASURES 非双曲遍历测度

Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0122

L. Díaz

{"title":"NONHYPERBOLIC ERGODIC MEASURES","authors":"L. Díaz","doi":"10.1142/9789813272880_0122","DOIUrl":"https://doi.org/10.1142/9789813272880_0122","url":null,"abstract":"We discuss some methods for constructing nonhyperbolic ergodic measures and their applications in the setting of nonhyperbolic skew-products, homoclinic classes, and robustly transitive diffeomorphisms. to Wellington de Melo in memoriam 1 The transitive and nonhyperbolic setting Irrational rotations of the circle T 1 and Anosov maps of the two-torus T 2 are emblematic examples of transitive systems (existence of a dense orbit). Small perturbations of Anosov systems are also transitive. This property fails however for irrational rotations. Anosov diffeomorphisms are also paradigmatic examples of hyperbolic maps and, by definition, hyperbolicity persists by small perturbations. Our focus are systems which are robustly transitive. In dimension three or higher, there are important examples of those systems that fail to be hyperbolic. They are one of the main foci of this paper. A second focus is on nonhyperbolic elementary pieces of dynamics. We discuss how their lack of hyperbolicity is reflected at the ergodic level by the existence of nonhyperbolic ergodic measures. We also study how this influences the structure of the space of measures. In this discussion, we see how this sort of dynamics gives rise to robust cycles and blenders. This research has been partially supported by CNE-Faperj and CNPq-grants (Brazil). The author warmly thanks J. Bochi, Ch. Bonatti, S. Crovisier, K. Gelfert, A. Gorodetski, Y. Ilyashenko, D. Kwietniak, J. Palis, M. Rams, A. Tahzibi, C. Vásques, and J. Yang for their useful comments and conversations. MSC2010: primary 37D25; secondary 37D30, 28D20, 28D99.","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"55 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":"125837269","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

FFT BASED SPECTRAL EWALD METHODS AS AN ALTERNATIVE TO FAST MULTIPOLE METHODS 基于FFT的光谱ewald方法作为快速多极方法的替代方法

Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0197

A. Tornberg

{"title":"FFT BASED SPECTRAL EWALD METHODS AS AN ALTERNATIVE TO FAST MULTIPOLE METHODS","authors":"A. Tornberg","doi":"10.1142/9789813272880_0197","DOIUrl":"https://doi.org/10.1142/9789813272880_0197","url":null,"abstract":"In this paper, we review a set of fast and spectrally accurate methods for rapid evaluation of three dimensional electrostatic and Stokes potentials. The algorithms use the so-called Ewald decomposition and are FFT-based, which makes them naturally most efficient for the triply periodic case. Two key ideas have allowed efficient extension of these Spectral Ewald (SE) methods to problems with periodicity in only one or two dimensions: an adaptive 3D FFT that apply different upsampling rates locally combined with a newmethod for FFT based solutions of free space harmonic and biharmonic problems. The latter approach is also used to extend to the free space case, with no periodicity. For the non-radial kernels of Stokes flow, the structure of their Fourier transform is exploited to extend the applicability from the radial harmonic and biharmonic kernels. Awindow function is convolvedwith the point charges to assign values on the FTT grid. Spectral accuracy is attained with a variable number of points in the support of the window function, tuning a shape parameter according to this choice. A new window function, recently introduced in the context of a non-uniform FFT algorithm, allows for further reduction in the computational time as compared to the truncated Gaussians previously used in the SE method.","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"52 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":"131486860","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