{"title":"Book Review: The Cremona group and its subgroups","authors":"I. Dolgachev","doi":"10.1090/bull/1774","DOIUrl":"https://doi.org/10.1090/bull/1774","url":null,"abstract":"","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48947132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Book Review: Singularities of mappings: The local behaviour of smooth and complex analytic mappings","authors":"J. Damon","doi":"10.1090/bull/1771","DOIUrl":"https://doi.org/10.1090/bull/1771","url":null,"abstract":"","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42846533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The “standard” historical narrative has it that: 1) applied mathematics emerged as an academic discipline in the United States only after, and as a result of, World War II; and 2) a major factor in this emergence was the presence of European émigré mathematicians. While this standard narrative is not wrong, it masks a key part of the picture, namely, the foundation for this development was laid within the context of the American Mathematical Society in the 1920s, 1930s, and 1940s.
{"title":"The American Mathematical Society and Applied Mathematics from the 1920s to the 1950s: A Revisionist Account","authors":"K. Parshall","doi":"10.1090/bull/1754","DOIUrl":"https://doi.org/10.1090/bull/1754","url":null,"abstract":"The “standard” historical narrative has it that: 1) applied mathematics emerged as an academic discipline in the United States only after, and as a result of, World War II; and 2) a major factor in this emergence was the presence of European émigré mathematicians. While this standard narrative is not wrong, it masks a key part of the picture, namely, the foundation for this development was laid within the context of the American Mathematical Society in the 1920s, 1930s, and 1940s.","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47237620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Book Review: Accuracy of mathematical models: Dimension reduction, homogenization, and simplification","authors":"A. L. Madureira","doi":"10.1090/bull/1769","DOIUrl":"https://doi.org/10.1090/bull/1769","url":null,"abstract":"","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45392631","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we introduce the electromechanical mathematical model of the human heart. After deriving it from physical first principles, we discuss its mathematical properties and the way numerical methods can be set up to obtain numerical approximations of the (otherwise unachievable) mathematical solutions. The major challenges that we need to face—e.g., possible lack of initial and boundary data, the trade off between increasing the accuracy of the numerical model and its computational complexity—are addressed. Numerical tests here presented have a twofold aim: to show that numerical solutions match the expected theoretical rate of convergence, and that our model can provide a preliminary valuable tool to face problems of clinical relevance.
{"title":"Modeling the cardiac electromechanical function: A mathematical journey","authors":"A. Quarteroni, L. Dede’, Francesco Regazzoni","doi":"10.1090/bull/1738","DOIUrl":"https://doi.org/10.1090/bull/1738","url":null,"abstract":"In this paper we introduce the electromechanical mathematical model of the human heart. After deriving it from physical first principles, we discuss its mathematical properties and the way numerical methods can be set up to obtain numerical approximations of the (otherwise unachievable) mathematical solutions. The major challenges that we need to face—e.g., possible lack of initial and boundary data, the trade off between increasing the accuracy of the numerical model and its computational complexity—are addressed. Numerical tests here presented have a twofold aim: to show that numerical solutions match the expected theoretical rate of convergence, and that our model can provide a preliminary valuable tool to face problems of clinical relevance.","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47879882","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Harold Widom Tribute","authors":"Ivan Corwin","doi":"10.1090/bull/1761","DOIUrl":"https://doi.org/10.1090/bull/1761","url":null,"abstract":"","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43193866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This is a brief review of the categorification of the Jones polynomial and its significance and ramifications in geometry, algebra, and low-dimensional topology.
本文简要回顾了琼斯多项式的分类及其在几何、代数和低维拓扑中的意义和分支。
{"title":"Categorical lifting of the Jones polynomial: a survey","authors":"M. Khovanov, Robert Lipshitz","doi":"10.1090/bull/1772","DOIUrl":"https://doi.org/10.1090/bull/1772","url":null,"abstract":"This is a brief review of the categorification of the Jones polynomial and its significance and ramifications in geometry, algebra, and low-dimensional topology.","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47190521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This is a survey of Harold Widom’s work in random matrices. We start with his pioneering papers on the sine-kernel determinant, continue with his and Craig Tracy’s groundbreaking results concerning the distribution functions of random matrix theory, touch on the remarkable universality of the Tracy–Widom distributions in mathematics and physics, and close with Tracy and Widom’s remarkable work on the asymmetric simple exclusion process.
{"title":"Harold Widom’s work in random matrix theory","authors":"Ivan Corwin, P. Deift, A. Its","doi":"10.1090/bull/1757","DOIUrl":"https://doi.org/10.1090/bull/1757","url":null,"abstract":"This is a survey of Harold Widom’s work in random matrices. We start with his pioneering papers on the sine-kernel determinant, continue with his and Craig Tracy’s groundbreaking results concerning the distribution functions of random matrix theory, touch on the remarkable universality of the Tracy–Widom distributions in mathematics and physics, and close with Tracy and Widom’s remarkable work on the asymmetric simple exclusion process.","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48818849","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This is a survey of Harold Widom’s work in Toeplitz operators, embracing his early results on the invertibility and spectral theory of Toeplitz operators, his investigations of the eigenvalue distribution of convolution operators, and his groundbreaking research into Toeplitz and Wiener–Hopf determinants.
{"title":"Harold Widom’s work in Toeplitz operators","authors":"E. Basor, A. Böttcher, T. Ehrhardt","doi":"10.1090/bull/1758","DOIUrl":"https://doi.org/10.1090/bull/1758","url":null,"abstract":"This is a survey of Harold Widom’s work in Toeplitz operators, embracing his early results on the invertibility and spectral theory of Toeplitz operators, his investigations of the eigenvalue distribution of convolution operators, and his groundbreaking research into Toeplitz and Wiener–Hopf determinants.","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43890710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Book Review: The Bellman function technique in harmonic analysis","authors":"Irina Holmes Fay","doi":"10.1090/bull/1759","DOIUrl":"https://doi.org/10.1090/bull/1759","url":null,"abstract":"","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42901599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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