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

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COHOMOLOGY OF ARITHMETIC GROUPS - FIELDS MEDAL LECTURE 算术群的上同调-领域奖章讲座
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0014
Akshay Venkatesh
{"title":"COHOMOLOGY OF ARITHMETIC GROUPS - FIELDS MEDAL LECTURE","authors":"Akshay Venkatesh","doi":"10.1142/9789813272880_0014","DOIUrl":"https://doi.org/10.1142/9789813272880_0014","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":"130761199","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
ON THE WORK OF AKSHAY VENKATESH 关于akshay venkatesh的工作
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0005
P. Sarnak
{"title":"ON THE WORK OF AKSHAY VENKATESH","authors":"P. Sarnak","doi":"10.1142/9789813272880_0005","DOIUrl":"https://doi.org/10.1142/9789813272880_0005","url":null,"abstract":"","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"226 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":"122695687","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
A PANORAMA OF SINGULAR SPDES 奇异蜘蛛的全景图
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0140
M. Gubinelli
{"title":"A PANORAMA OF SINGULAR SPDES","authors":"M. Gubinelli","doi":"10.1142/9789813272880_0140","DOIUrl":"https://doi.org/10.1142/9789813272880_0140","url":null,"abstract":"I will review the setting and some of the recent results in the field of singular stochastic partial differential equations (SSPDEs). Since Hairer’s invention of regularity structures this field has experienced a rapid development. SSPDEs are non-linear equations with random and irregular source terms which make them ill-posed in classical sense. Their study involves a tight interplay between stochastic analysis, analysis of PDEs (including paradifferential calculus) and algebra.","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"13 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":"121422847","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: 12
LESSON STUDY IN MATHEMATICS: CURRENT STATUS AND FURTHER DIRECTIONS 数学课程研究的现状与发展方向
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0040
Rongjin Huang, A. Takahashi, Stéphane Clivaz, Mercy Kazima, Maitree Inprasitha
{"title":"LESSON STUDY IN MATHEMATICS: CURRENT STATUS AND FURTHER DIRECTIONS","authors":"Rongjin Huang, A. Takahashi, Stéphane Clivaz, Mercy Kazima, Maitree Inprasitha","doi":"10.1142/9789813272880_0040","DOIUrl":"https://doi.org/10.1142/9789813272880_0040","url":null,"abstract":"","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"14 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":"117113009","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
HODGE THEORY AND CYCLE THEORY OF LOCALLY SYMMETRIC SPACES 局部对称空间的Hodge理论和循环理论
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0079
N. Bergeron
{"title":"HODGE THEORY AND CYCLE THEORY OF LOCALLY SYMMETRIC SPACES","authors":"N. Bergeron","doi":"10.1142/9789813272880_0079","DOIUrl":"https://doi.org/10.1142/9789813272880_0079","url":null,"abstract":"We discuss several results pertaining to the Hodge and cycle theories of locally symmetric spaces. The unity behind these results is motivated by a vague but fruitful analogy between locally symmetric spaces and projective varieties.","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"188 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":"117284747","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
CONSTRUCTING GROUP ACTIONS ON QUASI-TREES 拟树上群动作的构造
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0089
K. Fujiwara
{"title":"CONSTRUCTING GROUP ACTIONS ON QUASI-TREES","authors":"K. Fujiwara","doi":"10.1142/9789813272880_0089","DOIUrl":"https://doi.org/10.1142/9789813272880_0089","url":null,"abstract":"A quasi-tree is a geodesic metric space quasi-isometric to a tree. We give a general construction of many actions of groups on quasi-trees. The groups we can handle include non-elementary hyperbolic groups, CAT(0) groups with rank 1 elements, mapping class groups and the outer automorphism groups of free groups. As an application, we show that mapping class groups act on finite products of Gromov-hyperbolic spaces so that orbit maps are quasi-isometric embeddings. It implies that mapping class groups have finite asymptotic dimension.","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"112 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":"114352827","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
MULTISCALE ANALYSIS OF WAVE PROPAGATION IN RANDOM MEDIA 随机介质中波传播的多尺度分析
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0164
J. Garnier
{"title":"MULTISCALE ANALYSIS OF WAVE PROPAGATION IN RANDOM MEDIA","authors":"J. Garnier","doi":"10.1142/9789813272880_0164","DOIUrl":"https://doi.org/10.1142/9789813272880_0164","url":null,"abstract":"Wave propagation in random media can be studied by multiscale and stochastic analysis. We review some recent advances and their applications. In particular, in a physically relevant regime of separation of scales, wave propagation is governed by a Schrödinger-type equation driven by a Brownian field. We study the associated moment equations and describe the propagation of coherent and incoherent waves. We quantify the scintillation of the wave and the fluctuations of the Wigner distribution. These results make it possible to introduce and characterize correlation-based imaging methods. 1 Wave propagation in random media In many wave propagation scenarios the medium is not constant, but varies in a complicated fashion on a spatial scale that is small compared to the total propagation distance. This is the case for wave propagation through the turbulent atmosphere, the Earth’s crust, the ocean, and complex biological tissue for instance. If one aims to use transmitted or reflected waves for communication or imaging purposes it is important to characterize how such microstructure affects and corrupts the wave. Motivated by the situation described above we consider wave propagation through timeindependent complex media with a spatially varying index of refraction. Typically we cannot expect to know the index of refraction pointwise so we model it as a realization of a random process. When the index of refraction is a random process, the wave field is itself a random process and we are interested in how the statistics of the random medium affects the statistics of the wave field. The analysis of wave propagation in random media has a long history. It was first dealt with phenomenogical models such as the radiative transfer theory. The first mathematical papers were written in the 60’s by Keller [1964] who connected radiative transport theory and random wave equations. In the review presented at MSC2010: primary 35R60; secondary 35R30.","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"41 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":"124625056","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
ASYMPTOTIC EFFICIENCY IN HIGH-DIMENSIONAL COVARIANCE ESTIMATION 高维协方差估计的渐近效率
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0165
V. Koltchinskii
{"title":"ASYMPTOTIC EFFICIENCY IN HIGH-DIMENSIONAL COVARIANCE ESTIMATION","authors":"V. Koltchinskii","doi":"10.1142/9789813272880_0165","DOIUrl":"https://doi.org/10.1142/9789813272880_0165","url":null,"abstract":"","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"17 2 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":"116863226","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
CALCULUS, HEAT FLOW AND CURVATURE-DIMENSION BOUNDS IN METRIC MEASURE SPACES 度量空间中的微积分、热流和曲率维边界
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0015
L. Ambrosio
{"title":"CALCULUS, HEAT FLOW AND CURVATURE-DIMENSION BOUNDS IN METRIC MEASURE SPACES","authors":"L. Ambrosio","doi":"10.1142/9789813272880_0015","DOIUrl":"https://doi.org/10.1142/9789813272880_0015","url":null,"abstract":"The theory of curvature-dimension bounds for nonsmooth spaces has several motivations: the study of functional and geometric inequalities in structures which are very far from being Euclidean, therefore with new non-Riemannian tools, the description of the “closure” of classes of Riemannian manifolds under suitable geometric constraints, the stability of analytic and geometric properties of spaces (e.g. to prove rigidity results). Even though these goals may occasionally be in conflict, in the last few years we have seen spectacular developments in all these directions, and my text is meant both as a survey and as an introduction to this quickly developing research field.","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"11 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131858429","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: 104
GRADIENTS AND FLOWS: CONTINUOUS OPTIMIZATION APPROACHES TO THE MAXIMUM FLOW PROBLEM 梯度和流动:最大流量问题的连续优化方法
Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI: 10.1142/9789813272880_0185
A. Madry
{"title":"GRADIENTS AND FLOWS: CONTINUOUS OPTIMIZATION APPROACHES TO THE MAXIMUM FLOW PROBLEM","authors":"A. Madry","doi":"10.1142/9789813272880_0185","DOIUrl":"https://doi.org/10.1142/9789813272880_0185","url":null,"abstract":"We use the lens of the maximum flow problem, one of the most fundamental problems in algorithmic graph theory, to describe a new framework for design of graph algorithms. At a high level, this framework casts the graph problem at hand as a convex optimization task and then applies to it an appropriate method from the continuous optimization toolkit. We survey how this new approach led to the first in decades progress on the maximum flow problem and then briefly sketch the challenges that still remain.","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":"125625596","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
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