{"title":"Homological Methods in Commutative Algebra","authors":"Andrea Ferretti","doi":"10.1090/gsm/234","DOIUrl":"https://doi.org/10.1090/gsm/234","url":null,"abstract":"This essay provides a short introduction to the theme of the workshop.","PeriodicalId":140374,"journal":{"name":"Graduate Studies in Mathematics","volume":"132 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139319724","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}
{"title":"A First Course in Fractional Sobolev Spaces","authors":"G. Leoni","doi":"10.1090/gsm/229","DOIUrl":"https://doi.org/10.1090/gsm/229","url":null,"abstract":"This book provides a gentle introduction to fractional Sobolev spaces, which play a central role in the calculus of variations, partial differential equations, and harmonic analysis. The first part deals with fractional Sobolev spaces of one variable. It covers the definition, standard properties, extensions, embeddings, Hardy inequalities, and interpolation inequalities. The second part deals with fractional Sobolev spaces of several variables. The author studies completeness, density, homogeneous fractional Sobolev spaces, embeddings, necessary and sufficient conditions for extensions, Gagliardo-Nirenberg type interpolation inequalities, and trace theory. The third part explores some applications: interior regularity for the Poisson problem with the right-hand side in a fractional Sobolev space and some basic properties of the fractional Laplacian. The first part of the book is accessible to advanced undergraduates with a strong background in integration theory; the second part to graduate students having familiarity with measure and integration and some functional analysis. Basic knowledge of Sobolev spaces would help, but is not necessary. The book can also serve as a reference for mathematicians working in the calculus of variations and partial differential equations as well as for researchers in other disciplines with a solid mathematics background. It contains several exercises and is self-contained.","PeriodicalId":140374,"journal":{"name":"Graduate Studies in Mathematics","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116505720","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}
{"title":"Topological and Ergodic Theory of Symbolic Dynamics","authors":"H. Bruin","doi":"10.1090/gsm/228","DOIUrl":"https://doi.org/10.1090/gsm/228","url":null,"abstract":"","PeriodicalId":140374,"journal":{"name":"Graduate Studies in Mathematics","volume":"104 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134045300","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}
{"title":"A First Course in Spectral Theory","authors":"Milivoje Lukic","doi":"10.1090/gsm/226","DOIUrl":"https://doi.org/10.1090/gsm/226","url":null,"abstract":"","PeriodicalId":140374,"journal":{"name":"Graduate Studies in Mathematics","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121189955","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}
{"title":"Geometric Structures on Manifolds","authors":"W. Goldman","doi":"10.1090/gsm/227","DOIUrl":"https://doi.org/10.1090/gsm/227","url":null,"abstract":"The study of locally homogeneous geometric structures on manifolds was initiated by Charles Ehresmann in 1936, who first proposed the classification of putting a “classical geometry” on a topological manifold. In the late 1970’s, locally homogeneous Riemannian structures on 3-manifolds formed the context for Bill Thurston’s Geometrization Conjecture, later proved by Perelman. This book develops the theory of geometric structures modeled on a homogeneous space of a Lie group, which are not necessarily Riemannian. Drawing on a diverse collection of techniques, we hope to invite researchers at all levels to this fascinating and currently extremely active area of mathematics.","PeriodicalId":140374,"journal":{"name":"Graduate Studies in Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123878685","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}
{"title":"Groups and Topological Dynamics","authors":"V. Nekrashevych","doi":"10.1090/gsm/223","DOIUrl":"https://doi.org/10.1090/gsm/223","url":null,"abstract":"...","PeriodicalId":140374,"journal":{"name":"Graduate Studies in Mathematics","volume":"2011 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127359586","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}
{"title":"The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations","authors":"J. Bedrossian, V. Vicol","doi":"10.1090/gsm/225","DOIUrl":"https://doi.org/10.1090/gsm/225","url":null,"abstract":"","PeriodicalId":140374,"journal":{"name":"Graduate Studies in Mathematics","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129259769","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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