Pub Date : 2006-07-19DOI: 10.21711/217504322007/em131
Andrés Navas
{"title":"Grupos de difeomorfismos del círculo","authors":"Andrés Navas","doi":"10.21711/217504322007/em131","DOIUrl":"https://doi.org/10.21711/217504322007/em131","url":null,"abstract":"","PeriodicalId":359243,"journal":{"name":"Ensaios Matemáticos","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129792755","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}
Pub Date : 2004-03-22DOI: 10.21711/217504322004/em72
A. Oancea
The purpose of this paper is to give a survey of the various versions of Floer homology for manifolds with contact type boundary that have so far appeared in the literature. Under the name of ``Symplectic homology'' or ``Floer homology for manifolds with boundary'' they bear in fact common features and we shall try to underline the principles that unite them. Once this will be accomplished we shall proceed to describe the peculiarity of each of the constructions and the specific applications that unfold out of it: classification of ellipsoids and polydiscs in $mathbb{C}^n$, stability of the action spectrum for contact type boundaries of symplectic manifolds, existence of closed characteristics on contact type hypersurfaces and obstructions to exact Lagrange embeddings. The computation of the Floer cohomology for balls in $mathbb{C}^n$ is carried by explicitly perturbing the nondegenerate Morse-Bott spheres of closed characteristics.
{"title":"A survey of Floer homology for manifolds with contact type boundary or symplectic homology","authors":"A. Oancea","doi":"10.21711/217504322004/em72","DOIUrl":"https://doi.org/10.21711/217504322004/em72","url":null,"abstract":"The purpose of this paper is to give a survey of the various versions of Floer homology for manifolds with contact type boundary that have so far appeared in the literature. Under the name of ``Symplectic homology'' or ``Floer homology for manifolds with boundary'' they bear in fact common features and we shall try to underline the principles that unite them. Once this will be accomplished we shall proceed to describe the peculiarity of each of the constructions and the specific applications that unfold out of it: classification of ellipsoids and polydiscs in $mathbb{C}^n$, stability of the action spectrum for contact type boundaries of symplectic manifolds, existence of closed characteristics on contact type hypersurfaces and obstructions to exact Lagrange embeddings. The computation of the Floer cohomology for balls in $mathbb{C}^n$ is carried by explicitly perturbing the nondegenerate Morse-Bott spheres of closed characteristics.","PeriodicalId":359243,"journal":{"name":"Ensaios Matemáticos","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121384349","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}
Pub Date : 1900-01-01DOI: 10.21711/217504322009/em171
A. Arbieto, C. Matheus, C. Moreira
The main goal of this survey is the description of the fruitful interaction between Ergodic Theory and Number Theory via the study of two beautiful results: the first one by Ben Green and Terence Tao (about long arithmetic progressions of primes) and the second one by Noam Elkies and Curtis McMullen (about the distribution of the sequence { √ n} mod 1). More precisely, during the first part, we will see how the ergodic-theoretical ideas of Furstenberg about the famous Szemeredi theorem were greatly generalized by Green and Tao in order to solve the classical problem of finding arbitrarily long arithmetical progression of prime numbers, while the second part will focus on how Elkies and McMullen used the ideas of Ratner's theory (about the classification of ergodic measures related to unipotent dynamics) to compute explicitly the distribution of the sequence { √ n} on the unit circle.
{"title":"The remarkable effectiveness of ergodic theory in number theory","authors":"A. Arbieto, C. Matheus, C. Moreira","doi":"10.21711/217504322009/em171","DOIUrl":"https://doi.org/10.21711/217504322009/em171","url":null,"abstract":"The main goal of this survey is the description of the fruitful interaction between Ergodic Theory and Number Theory via the study of two beautiful results: the first one by Ben Green and Terence Tao (about long arithmetic progressions of primes) and the second one by Noam Elkies and Curtis McMullen (about the distribution of the sequence { √ n} mod 1). More precisely, during the first part, we will see how the ergodic-theoretical ideas of Furstenberg about the famous Szemeredi theorem were greatly generalized by Green and Tao in order to solve the classical problem of finding arbitrarily long arithmetical progression of prime numbers, while the second part will focus on how Elkies and McMullen used the ideas of Ratner's theory (about the classification of ergodic measures related to unipotent dynamics) to compute explicitly the distribution of the sequence { √ n} on the unit circle.","PeriodicalId":359243,"journal":{"name":"Ensaios Matemáticos","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132895657","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}
Pub Date : 1900-01-01DOI: 10.21711/217504322014/em261
S. Pigola, A. G. Setti
These lecture notes contain, in a slightly expanded form, the material presented at the Summer School in Dierential Geometry held in
这些课堂讲稿包含，以稍微扩展的形式，在微分几何暑期学校举行的材料
{"title":"Global divergence theorems in nonlinear PDEs and geometry","authors":"S. Pigola, A. G. Setti","doi":"10.21711/217504322014/em261","DOIUrl":"https://doi.org/10.21711/217504322014/em261","url":null,"abstract":"These lecture notes contain, in a slightly expanded form, the material presented at the Summer School in Dierential Geometry held in","PeriodicalId":359243,"journal":{"name":"Ensaios Matemáticos","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124102748","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}
Pub Date : 1900-01-01DOI: 10.21711/217504322005/em101
Y. Ollivier
Random groups provide a rigorous way to tackle such questions as “What does a typical (finitely generated) group look like?” or “What is the behavior of an element of a group when nothing particular happens?” We review the results obtained on random groups as of January 2005. We give proper definitions and list known properties of typical groups. We also emphasize properties of random elements in a given group. In addition we present more specific, randomly twisted group constructions providing new, “wild” examples of groups. A comprehensive discussion of open problems and perspectives is included. 2000 Mathematics Subject Classification: 20F65, 20P05, 60B99, 20F05, 20F67.
{"title":"A January 2005 invitation to random groups","authors":"Y. Ollivier","doi":"10.21711/217504322005/em101","DOIUrl":"https://doi.org/10.21711/217504322005/em101","url":null,"abstract":"Random groups provide a rigorous way to tackle such questions as “What does a typical (finitely generated) group look like?” or “What is the behavior of an element of a group when nothing particular happens?” We review the results obtained on random groups as of January 2005. We give proper definitions and list known properties of typical groups. We also emphasize properties of random elements in a given group. In addition we present more specific, randomly twisted group constructions providing new, “wild” examples of groups. A comprehensive discussion of open problems and perspectives is included. 2000 Mathematics Subject Classification: 20F65, 20P05, 60B99, 20F05, 20F67.","PeriodicalId":359243,"journal":{"name":"Ensaios Matemáticos","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114946540","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}
Pub Date : 1900-01-01DOI: 10.21711/217504322019/em341
D. Nualart
{"title":"Malliavin calculus and normal approximations","authors":"D. Nualart","doi":"10.21711/217504322019/em341","DOIUrl":"https://doi.org/10.21711/217504322019/em341","url":null,"abstract":"","PeriodicalId":359243,"journal":{"name":"Ensaios Matemáticos","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116961879","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}
Pub Date : 1900-01-01DOI: 10.21711/217504322010/em191
Olivier Druet
{"title":"La notion de stabilité pour des équations aux dérivées partielles elliptiques","authors":"Olivier Druet","doi":"10.21711/217504322010/em191","DOIUrl":"https://doi.org/10.21711/217504322010/em191","url":null,"abstract":"","PeriodicalId":359243,"journal":{"name":"Ensaios Matemáticos","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133274321","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}
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