This survey article is the written version of a talk given at the Bourbaki seminar in April 2021. We give an introduction to Zagier's conjecture on special values of Dedekind zeta functions, and its relation to $K$-theory of fields and the theory of motives. We survey recent progress on the conjecture and in particular the proof of the $n=4$ case of the conjecture by Goncharov and Rudenko.
{"title":"Exposé Bourbaki 1176 : Progrès récents sur la conjecture de Zagier et le programme de Goncharov (d'après Goncharov, Rudenko, Gangl,...)","authors":"C. Dupont","doi":"10.24033/ast.1165","DOIUrl":"https://doi.org/10.24033/ast.1165","url":null,"abstract":"This survey article is the written version of a talk given at the Bourbaki seminar in April 2021. We give an introduction to Zagier's conjecture on special values of Dedekind zeta functions, and its relation to $K$-theory of fields and the theory of motives. We survey recent progress on the conjecture and in particular the proof of the $n=4$ case of the conjecture by Goncharov and Rudenko.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47559611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The convex-cocompact subgroups are central in hyperbolic geometry and more generally in negative curvature. Labourie introduced in 2005 the notion of 'Anosov' subgroup which proves progressively to be the right generalizations of convex-cocompact groups, especially after the works of Kapovich, Leeb and Porti. This expose will review different caracteriations of those groups, emphasizing the parallel (or difference) with the negative curvature, and will give their basic properties.
{"title":"Groupes convexes-cocompacts en rang supérieur","authors":"Olivier Guichard","doi":"10.24033/ast.1082","DOIUrl":"https://doi.org/10.24033/ast.1082","url":null,"abstract":"The convex-cocompact subgroups are central in hyperbolic geometry and more generally in negative curvature. Labourie introduced in 2005 the notion of 'Anosov' subgroup which proves progressively to be the right generalizations of convex-cocompact groups, especially after the works of Kapovich, Leeb and Porti. This expose will review different caracteriations of those groups, emphasizing the parallel (or difference) with the negative curvature, and will give their basic properties.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2020-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45015229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the minima of Markov and Lagrange Dynamical Spectra","authors":"Carlos Gustavo MOREIRA","doi":"10.24033/ast.1099","DOIUrl":"https://doi.org/10.24033/ast.1099","url":null,"abstract":"","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68829511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Hedgehogs in higher dimensions and their applications","authors":"Mikhail LYUBICH, Remus RADU, Raluca TANASE","doi":"10.24033/ast.1115","DOIUrl":"https://doi.org/10.24033/ast.1115","url":null,"abstract":"","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68829986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
For partially hyperbolic diffeomorphisms with 2-dimensional center, accessibility is C1-stable. Moreover, for center bunched skew-products (stable) accessibility is C1-dense.
{"title":"Stable accessibility with 2-dimensional center","authors":"A. Avila, M. Viana","doi":"10.24033/ast.1117","DOIUrl":"https://doi.org/10.24033/ast.1117","url":null,"abstract":"For partially hyperbolic diffeomorphisms with 2-dimensional center, accessibility is C1-stable. Moreover, for center bunched skew-products (stable) accessibility is C1-dense.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":"416 1","pages":"301-320"},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68830067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jr. David A. VOGAN, Jeffrey D. ADAMS, Peter E. TRAPA, Marc A.A. van Leeuwen
{"title":"Unitary representations of real reductive groups","authors":"Jr. David A. VOGAN, Jeffrey D. ADAMS, Peter E. TRAPA, Marc A.A. van Leeuwen","doi":"10.24033/ast.1119","DOIUrl":"https://doi.org/10.24033/ast.1119","url":null,"abstract":"","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68830115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Fixed points of nilpotent actions on R²","authors":"Sebastião FIRMO, Patrice Le Calvez, Javier RIBON","doi":"10.24033/ast.1102","DOIUrl":"https://doi.org/10.24033/ast.1102","url":null,"abstract":"","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68829572","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sylvain CROVISIER (éd.), Raphaël KRIKORIAN (éd.), Carlos MATHEUS (éd.), Samuel SENTI (éd.)
{"title":"Quelques aspects de la théorie des systèmes dynamiques : un hommage à Jean-Christophe Yoccoz (volume II)","authors":"Sylvain CROVISIER (éd.), Raphaël KRIKORIAN (éd.), Carlos MATHEUS (éd.), Samuel SENTI (éd.)","doi":"10.24033/ast.1108","DOIUrl":"https://doi.org/10.24033/ast.1108","url":null,"abstract":"","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68829713","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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