{"title":"Variétés en expansion (d’après M. Gromov, L. Guth, ...)","authors":"N. Bergeron","doi":"10.24033/ast.1070","DOIUrl":"https://doi.org/10.24033/ast.1070","url":null,"abstract":"","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68828420","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":"Noeuds, mouvements de Reidemeister et algorithmes (d’après Lackenby)","authors":"Arnaud de MESMAY","doi":"10.24033/ast.1059","DOIUrl":"https://doi.org/10.24033/ast.1059","url":null,"abstract":"","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68828046","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":"Inégalités isopérimétriques dans les espaces métriques mesurés (d’après F. Cavalletti & A. Mondino)","authors":"Cédric VILLANI","doi":"10.24033/ast.1065","DOIUrl":"https://doi.org/10.24033/ast.1065","url":null,"abstract":"","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":"41 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68828790","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":"Splendeur des variétés de Deligne-Lusztig","authors":"Olivier DUDAS","doi":"10.24033/ast.1081","DOIUrl":"https://doi.org/10.24033/ast.1081","url":null,"abstract":"","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":"76 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68829037","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":"Derived Grothendieck-Teichmüller group and graph complexes, (after T. Willwacher)","authors":"Maxim KONTSEVICH","doi":"10.24033/ast.1064","DOIUrl":"https://doi.org/10.24033/ast.1064","url":null,"abstract":"","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68828316","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":"Dynamique de l'équation de Schrödinger sur le disque","authors":"Gabriel RIVIERE","doi":"10.24033/ast.1089","DOIUrl":"https://doi.org/10.24033/ast.1089","url":null,"abstract":"","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":"144 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68828893","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}
where Ω ⊂ R is some open set, u : Ω → R is a convex function, and the function f : Ω× R× R → R is given. In other words, the Monge-Ampère equation prescribes the product of the eigenvalues of the Hessian of u, in contrast with the “model” elliptic equation ∆u = f which prescribes their sum. As we shall explain later, the convexity of the solution u is a necessary condition to make the equation degenerate elliptic, and therefore to hope for regularity results. The goal of this note is to give first a general overview of the classical theory, and then discuss some recent important developments on this beautiful topic. For our presentation of the classical theory, we follow the survey paper [25].
{"title":"On the Monge-Ampère equation","authors":"Alessio FIGALLI","doi":"10.24033/ast.1092","DOIUrl":"https://doi.org/10.24033/ast.1092","url":null,"abstract":"where Ω ⊂ R is some open set, u : Ω → R is a convex function, and the function f : Ω× R× R → R is given. In other words, the Monge-Ampère equation prescribes the product of the eigenvalues of the Hessian of u, in contrast with the “model” elliptic equation ∆u = f which prescribes their sum. As we shall explain later, the convexity of the solution u is a necessary condition to make the equation degenerate elliptic, and therefore to hope for regularity results. The goal of this note is to give first a general overview of the classical theory, and then discuss some recent important developments on this beautiful topic. For our presentation of the classical theory, we follow the survey paper [25].","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68829645","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}
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. L’inégalité de corrélation gaussienne, d’après Thomas Royen Franck Barthe
{"title":"L’inégalité de corrélation gaussienne (d’après Thomas Royen)","authors":"F. Barthe","doi":"10.24033/ast.1062","DOIUrl":"https://doi.org/10.24033/ast.1062","url":null,"abstract":"HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. L’inégalité de corrélation gaussienne, d’après Thomas Royen Franck Barthe","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68828240","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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