{"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}
{"title":"Renormalization in Quantum Field Theory (after R. Borcherds)","authors":"Estanislao HERSCOVICH","doi":"10.24033/ast.1078","DOIUrl":"https://doi.org/10.24033/ast.1078","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":"68829183","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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