Pub Date : 1900-01-01DOI: 10.21711/217504322023/em384
C. Boldrighini, S. Frigio, P. Maponi, A. Pellegrinotti, Y. Sinai
{"title":"Real and complex Li-Sinai solutions of the 3D incompressible Navier-Stokes equations","authors":"C. Boldrighini, S. Frigio, P. Maponi, A. Pellegrinotti, Y. Sinai","doi":"10.21711/217504322023/em384","DOIUrl":"https://doi.org/10.21711/217504322023/em384","url":null,"abstract":"","PeriodicalId":359243,"journal":{"name":"Ensaios Matemáticos","volume":"31 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":"132634993","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: 10.21711/217504322016/em304
J. Collins
A Seifert surface of a knot or link inS 3 is an oriented surface in S 3 whose boundary coincides with that of the link. A corresponding Seifert matrix has as its entries the linking numbers of a set of homology generators of the surface. Thus a Seifert matrix encodes essential information about the structure of a link and, unsurprisingly, can be used to dene powerful invariants, such as the Alexander polynomial. The program SeifertView has been designed to visualise Seifert surfaces given by braid representations, but it does not give the user any technical information about the knot or link. This article describes an algorithm which could work alongside SeifertView and compute a Seifert matrix from the same braids and surfaces. It also calculates the genus of the surface, the Alexander polynomial of the knot and the signature of the knot.
{"title":"An algorithm for computing the Seifert matrix of a link from a braid representation","authors":"J. Collins","doi":"10.21711/217504322016/em304","DOIUrl":"https://doi.org/10.21711/217504322016/em304","url":null,"abstract":"A Seifert surface of a knot or link inS 3 is an oriented surface in S 3 whose boundary coincides with that of the link. A corresponding Seifert matrix has as its entries the linking numbers of a set of homology generators of the surface. Thus a Seifert matrix encodes essential information about the structure of a link and, unsurprisingly, can be used to dene powerful invariants, such as the Alexander polynomial. The program SeifertView has been designed to visualise Seifert surfaces given by braid representations, but it does not give the user any technical information about the knot or link. This article describes an algorithm which could work alongside SeifertView and compute a Seifert matrix from the same braids and surfaces. It also calculates the genus of the surface, the Alexander polynomial of the knot and the signature of the knot.","PeriodicalId":359243,"journal":{"name":"Ensaios Matemáticos","volume":"19 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":"115250153","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: 10.21711/217504322013/em241
Vincent Borrelli, S. Jabrane, F. Lazarus, B. Thibert
This memoir is concerned with isometric embeddings of a square at torus in the three dimensional Euclidean space. The existence of such embeddings was proved by John Nash and Nicolaas Kuiper in the mid 50s. However, the geometry of these embeddings could barely be conceived from their original papers. Here we provide an explicit construction based on the convex integration theory introduced by Mikhail Gromov in the 70s. We then turn this construction into a computer implementation leading us to the visualisation of an isometrically embedded at torus. The pictures reveal a geometric object in-between fractals and ordinary surfaces. We call this object a C 1 fractal.
{"title":"Isometric embeddings of the square flat torus in ambient space","authors":"Vincent Borrelli, S. Jabrane, F. Lazarus, B. Thibert","doi":"10.21711/217504322013/em241","DOIUrl":"https://doi.org/10.21711/217504322013/em241","url":null,"abstract":"This memoir is concerned with isometric embeddings of a square at torus in the three dimensional Euclidean space. The existence of such embeddings was proved by John Nash and Nicolaas Kuiper in the mid 50s. However, the geometry of these embeddings could barely be conceived from their original papers. Here we provide an explicit construction based on the convex integration theory introduced by Mikhail Gromov in the 70s. We then turn this construction into a computer implementation leading us to the visualisation of an isometrically embedded at torus. The pictures reveal a geometric object in-between fractals and ordinary surfaces. We call this object a C 1 fractal.","PeriodicalId":359243,"journal":{"name":"Ensaios Matemáticos","volume":"6 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":"122326635","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: 10.21711/217504322013/em231
A. Teixeira, J. Černý
We review and comment recent research on random interlacements model introduced by A.-S. Sznitman in [43]. A particular emphasis is put on motivating the definition of the model via natural questions concerning geometrical/percolative properties of random walk trajectories on finite graphs, as well as on presenting some important techniques used in random interlacements’ literature in the most accessible way. This text is an expanded version of the lecture notes for the mini-course given at the XV Brazilian School of Probability in 2011. 2000 Mathematics Subject Classification: 60G50, 60K35, 82C41, 05C80.
{"title":"From random walk trajectories to random interlacements","authors":"A. Teixeira, J. Černý","doi":"10.21711/217504322013/em231","DOIUrl":"https://doi.org/10.21711/217504322013/em231","url":null,"abstract":"We review and comment recent research on random interlacements model introduced by A.-S. Sznitman in [43]. A particular emphasis is put on motivating the definition of the model via natural questions concerning geometrical/percolative properties of random walk trajectories on finite graphs, as well as on presenting some important techniques used in random interlacements’ literature in the most accessible way. This text is an expanded version of the lecture notes for the mini-course given at the XV Brazilian School of Probability in 2011. 2000 Mathematics Subject Classification: 60G50, 60K35, 82C41, 05C80.","PeriodicalId":359243,"journal":{"name":"Ensaios Matemáticos","volume":"29 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":"133746912","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: 10.21711/217504322006/em111
N. Bergeron
This volume is intended as an expository account of some re- sults and problems concerning the cohomology of locally symmetric spaces (especially arithmetic ones) and the relationship with the spectral theory of automorphic forms. The discussion is divided into four chapters: { A general introduction to arithmetic manifolds, Matsushima's formula and cohomological representations; { Cohomology of hyperbolic manifolds; { Isolation properties in the automorphic spectrum; { Cohomology of arithmetic manifolds. However this presentation will be very unbalanced: it is a slightly revised version of my habilitation thesis. It is nevertheless my hope that the reader will not be too much disappointed by the incompleteness of this acount and hopefully nd it useful.
{"title":"Sur la cohomologie et le spectre des variétés localement symétriques","authors":"N. Bergeron","doi":"10.21711/217504322006/em111","DOIUrl":"https://doi.org/10.21711/217504322006/em111","url":null,"abstract":"This volume is intended as an expository account of some re- sults and problems concerning the cohomology of locally symmetric spaces (especially arithmetic ones) and the relationship with the spectral theory of automorphic forms. The discussion is divided into four chapters: { A general introduction to arithmetic manifolds, Matsushima's formula and cohomological representations; { Cohomology of hyperbolic manifolds; { Isolation properties in the automorphic spectrum; { Cohomology of arithmetic manifolds. However this presentation will be very unbalanced: it is a slightly revised version of my habilitation thesis. It is nevertheless my hope that the reader will not be too much disappointed by the incompleteness of this acount and hopefully nd it useful.","PeriodicalId":359243,"journal":{"name":"Ensaios Matemáticos","volume":"79 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":"121308767","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: 10.21711/217504321989/em11
B. Malgrange
{"title":"Équations différentielles linéaires et transformation de Fourier : une introduction","authors":"B. Malgrange","doi":"10.21711/217504321989/em11","DOIUrl":"https://doi.org/10.21711/217504321989/em11","url":null,"abstract":"","PeriodicalId":359243,"journal":{"name":"Ensaios Matemáticos","volume":"66 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":"114887673","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: 10.21711/217504322023/em383
L. Bertini, D. Gabrielli, C. Landim
{"title":"Large deviations for diffusions: Donsker and Varadhan meet Freidlin and Wentzell","authors":"L. Bertini, D. Gabrielli, C. Landim","doi":"10.21711/217504322023/em383","DOIUrl":"https://doi.org/10.21711/217504322023/em383","url":null,"abstract":"","PeriodicalId":359243,"journal":{"name":"Ensaios Matemáticos","volume":"1 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":"129029225","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: 10.21711/217504322007/em121
R. Ruggiero
Manifolds with no conjugate points are natural generalizations of manifolds with nonpositive sectional curvatures. They have in common the fact that geodesics are global minimizers, a variational property of geodesics that is quite special. The restriction on the sign of the sectional curvatures of the manifold leads to a deep knowledge about the topology and the global geometry of the manifold, like the characterization of higher rank, nonpositively curved spaces as symmetric spaces. However, if we drop the assumptions concerning the local geometry of the manifold the study of geodesics becomes much harder. The purpose of this survey is to give an overview of the classical theory of manifolds without conjugate points where no assumptions are made on the sign of the sectional curvatures, since the famous work of Morse about minimizing geodesics of surfaces and the works of Hopf about tori without conjugate points. We shall show important classical and recent applications of many tools of Riemannian geometry, topological dynamics, geometric group theory and topology to study the geodesic flow of manifolds without conjugate points and its connections with the global geometry of the manifold. Such applications roughly show that manifolds without conjugate points are in many respects close to manifolds with nonpositive curvature from the topological point of view.
{"title":"Dynamics and global geometry of manifolds without conjugate points","authors":"R. Ruggiero","doi":"10.21711/217504322007/em121","DOIUrl":"https://doi.org/10.21711/217504322007/em121","url":null,"abstract":"Manifolds with no conjugate points are natural generalizations of manifolds with nonpositive sectional curvatures. They have in common the fact that geodesics are global minimizers, a variational property of geodesics that is quite special. The restriction on the sign of the sectional curvatures of the manifold leads to a deep knowledge about the topology and the global geometry of the manifold, like the characterization of higher rank, nonpositively curved spaces as symmetric spaces. However, if we drop the assumptions concerning the local geometry of the manifold the study of geodesics becomes much harder. The purpose of this survey is to give an overview of the classical theory of manifolds without conjugate points where no assumptions are made on the sign of the sectional curvatures, since the famous work of Morse about minimizing geodesics of surfaces and the works of Hopf about tori without conjugate points. We shall show important classical and recent applications of many tools of Riemannian geometry, topological dynamics, geometric group theory and topology to study the geodesic flow of manifolds without conjugate points and its connections with the global geometry of the manifold. Such applications roughly show that manifolds without conjugate points are in many respects close to manifolds with nonpositive curvature from the topological point of view.","PeriodicalId":359243,"journal":{"name":"Ensaios Matemáticos","volume":"44 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":"121586258","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：