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Vaughan Jones (1952–2020) 沃恩·琼斯(1952-2020)
L’Enseignement Mathématique Pub Date : 2023-06-08 DOI: 10.4171/lem/1044
Pierre de la Harpe, Anders Karlsson, T. Nagnibeda, F. Rădulescu
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引用次数: 0
Commission Internationale de l’Enseignement Mathématique. Once upon a time . . . Historical vignettes from the Archives of ICMI: The Aarhus ICMI-seminar on the teaching of geometry 国际数学教育委员会。《童话镇》……来自ICMI档案的历史缩略图:奥尔胡斯ICMI几何教学研讨会
L’Enseignement Mathématique Pub Date : 2022-07-08 DOI: 10.4171/lem/1039
Bernard R. Hodgson
{"title":"Commission Internationale de l’Enseignement Mathématique. Once upon a time . . . Historical vignettes from the Archives of ICMI: The Aarhus ICMI-seminar on the teaching of geometry","authors":"Bernard R. Hodgson","doi":"10.4171/lem/1039","DOIUrl":"https://doi.org/10.4171/lem/1039","url":null,"abstract":"","PeriodicalId":344085,"journal":{"name":"L’Enseignement Mathématique","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134599958","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
Commission Internationale de l’Enseignement Mathématique. Once upon a time ... Historical vignettes from the Archives of ICMI: The IMU centennial 国际宇航组织委员会。从前……ICMI档案中的历史片段:IMU百年纪念
L’Enseignement Mathématique Pub Date : 2022-04-20 DOI: 10.4171/lem/1028
Bernard R. Hodgson
{"title":"Commission Internationale de l’Enseignement Mathématique. Once upon a time ... Historical vignettes from the Archives of ICMI: The IMU centennial","authors":"Bernard R. Hodgson","doi":"10.4171/lem/1028","DOIUrl":"https://doi.org/10.4171/lem/1028","url":null,"abstract":"","PeriodicalId":344085,"journal":{"name":"L’Enseignement Mathématique","volume":"133 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130998539","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
Notes on Maskit’s Planarity Theorem 关于Maskit的平面性定理的注解
L’Enseignement Mathématique Pub Date : 2022-04-12 DOI: 10.4171/lem/1019
B. Bowditch
{"title":"Notes on Maskit’s Planarity Theorem","authors":"B. Bowditch","doi":"10.4171/lem/1019","DOIUrl":"https://doi.org/10.4171/lem/1019","url":null,"abstract":". We give an account of the Planarity Theorem of Maskit. This gives a classification of finitely generated groups acting effectively properly discontinuously by orientation-preserving homeomorphisms on a planar surface. One can also realise such groups as kleinian function groups. We also explain how one can give another proof of the planarity theorem using Dunwoody’s theory of tracks.","PeriodicalId":344085,"journal":{"name":"L’Enseignement Mathématique","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130991052","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
Residues of connections and the Chevalley–Weil formula for curves 曲线的连接残数与Chevalley-Weil公式
L’Enseignement Mathématique Pub Date : 2022-04-09 DOI: 10.4171/lem/1030
D. Arapura
{"title":"Residues of connections and the Chevalley–Weil formula for curves","authors":"D. Arapura","doi":"10.4171/lem/1030","DOIUrl":"https://doi.org/10.4171/lem/1030","url":null,"abstract":". Given a finite group of automorphisms of a compact Riemann sur- face, the Chevalley-Weil formula computes the character valued Euler characteristic of an equivariant line bundle. The goal of this article is to give a proof by computing using residues of a Gauss-Manin connection.","PeriodicalId":344085,"journal":{"name":"L’Enseignement Mathématique","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128360751","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
Compactifications of horospheric products 星形球积的紧化
L’Enseignement Mathématique Pub Date : 2022-04-08 DOI: 10.4171/LEM/1025
Behrang Forghani, Keivan Mallahi-Karai
{"title":"Compactifications of horospheric products","authors":"Behrang Forghani, Keivan Mallahi-Karai","doi":"10.4171/LEM/1025","DOIUrl":"https://doi.org/10.4171/LEM/1025","url":null,"abstract":". We define and study a new compactification, called the height compactification of the horospheric product of two infinite trees. We will provide a complete description of this compactification. In particular, we show that this compactification is isomorphic to the Busemann compactification when all the vertices of both trees have degree at least three, which also leads to a precise description of the Busemann functions in terms of the points in the geometric compactification of each tree. We will discuss an application to the asymptotic behavior of integrable ergodic cocycles with values in the isometry group of such horospheric product.","PeriodicalId":344085,"journal":{"name":"L’Enseignement Mathématique","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123190974","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
Binary subgroups of direct products 直积的二元子群
L’Enseignement Mathématique Pub Date : 2022-02-04 DOI: 10.4171/lem/1057
M. Bridson
{"title":"Binary subgroups of direct products","authors":"M. Bridson","doi":"10.4171/lem/1057","DOIUrl":"https://doi.org/10.4171/lem/1057","url":null,"abstract":"We explore an elementary construction that produces finitely presented groups with diverse homological finiteness properties -- the {em binary subgroups}, $B(Sigma,mu)<G_1timesdotstimes G_m$. These full subdirect products require strikingly few generators. If each $G_i$ is finitely presented, $B(Sigma,mu)$ is finitely presented. When the $G_i$ are non-abelian limit groups (e.g. free or surface groups), the $B(Sigma,mu)$ provide new examples of finitely presented, residually-free groups that do not have finite classifying spaces and are not of Stallings-Bieri type. These examples settle a question of Minasyan relating different notions of rank for residually-free groups. Using binary subgroups, we prove that if $G_1,dots,G_m$ are perfect groups, each requiring at most $r$ generators, then $G_1timesdotstimes G_m$ requires at most $r lfloor log_2 m+1 rfloor$ generators.","PeriodicalId":344085,"journal":{"name":"L’Enseignement Mathématique","volume":"122 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123938368","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
An inequality for non-microstates free entropy dimension for crossed products by finite abelian groups 有限阿贝尔群交叉积的非微观态自由熵维不等式
L’Enseignement Mathématique Pub Date : 2022-01-24 DOI: 10.4171/lem/1056
D. Shlyakhtenko
{"title":"An inequality for non-microstates free entropy dimension for crossed products by finite abelian groups","authors":"D. Shlyakhtenko","doi":"10.4171/lem/1056","DOIUrl":"https://doi.org/10.4171/lem/1056","url":null,"abstract":"For certain generating sets of the subfactor pair $Msubset Mrtimes G$ where $G$ is a finite abelian group we prove an approximate inequality between their non-microstates free entropy dimension, resembling the Shreier formula for ranks of finite index subgroups of free groups. As an application, we give bounds on free entropy dimension of generating sets of crossed products of the form $Mrtimes(mathbb{Z}/2mathbb{Z})^{oplusinfty}$ for a large class of algebras $M$.","PeriodicalId":344085,"journal":{"name":"L’Enseignement Mathématique","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134006262","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
Matrix bispectrality and noncommutative algebras: Beyond the prolate spheroidals 矩阵双谱性与非交换代数:超越长球面
L’Enseignement Mathématique Pub Date : 2022-01-22 DOI: 10.4171/lem/1053
F. Grunbaum, Brian D. Vasquez, J. Zubelli
{"title":"Matrix bispectrality and noncommutative algebras: Beyond the prolate spheroidals","authors":"F. Grunbaum, Brian D. Vasquez, J. Zubelli","doi":"10.4171/lem/1053","DOIUrl":"https://doi.org/10.4171/lem/1053","url":null,"abstract":"The bispectral problem is motivated by an effort to understand and extend a remarkable phenomenon in Fourier analysis on the real line: the operator of time-and-band limiting is an integral operator admitting a second-order differential operator with a simple spectrum in its commutator. In this article, we discuss a noncommutative version of the bispectral problem, obtained by allowing all objects in the original formulation to be matrix-valued. Deep attention is given to bispectral algebras and their presentations as a tool to get information about bispectral triples.","PeriodicalId":344085,"journal":{"name":"L’Enseignement Mathématique","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133956764","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
Spectral gap and strict outerness for actions of locally compact groups on full factors 全因子上局部紧群作用的谱隙和严格外度
L’Enseignement Mathématique Pub Date : 2022-01-04 DOI: 10.4171/lem/1054
A. Marrakchi, S. Vaes
{"title":"Spectral gap and strict outerness for actions of locally compact groups on full factors","authors":"A. Marrakchi, S. Vaes","doi":"10.4171/lem/1054","DOIUrl":"https://doi.org/10.4171/lem/1054","url":null,"abstract":"We prove that an outer action of a locally compact group $G$ on a full factor $M$ is automatically strictly outer, meaning that the relative commutant of $M$ in the crossed product is trivial. If moreover the image of $G$ in the outer automorphism group $operatorname{Out} M$ is closed, we prove that the crossed product remains full. We obtain this result by proving that the inclusion of $M$ in the crossed product automatically has a spectral gap property. Such results had only been proven for actions of discrete groups and for actions of compact groups, by using quite different methods in both cases. Even for the canonical Bogoljubov actions on free group factors or free Araki-Woods factors, these results are new.","PeriodicalId":344085,"journal":{"name":"L’Enseignement Mathématique","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126230009","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
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