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Synopsis
One of the famous 23 mathematics problems Hilbert formulated in 1900, the problem asks for a topological description of Lie groups without any direct reference to smooth structure. In notes from a graduate course he taught in 2011 with some extra material from his blog, Tao develops the machinery needed to solve Hilbert's fifth problem, and then uses it to classify approximate groups and finally to develop applications such as Gromov's celebrated theorem. The first part of the book can be used in a one-quarter or one-semester advanced graduate course. It assumes familiarity with basic graduate real analysis and linear algebra. The second part contains additional material that may be but need not be used for the course. Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)
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About the Author
Terence Tao was the winner of the 2014 Breakthrough Prize in Mathematics. He is the James and Carol Collins Chair of mathematics at UCLA and the youngest person ever to be promoted to full professor at the age of 24. In 2006 Tao became the youngest ever mathematician to win the Fields Medal. His other honours include the George Polya Prize from the Society for Industrial and Applied Mathematics (2010), the Alan T Waterman Award from the National Science Foundation (2008), the SASTRA Ramanujan Prize (2006), the Clay Research Award from the Clay Mathematical Institute (2003), the Bocher Memorial Prize from the American Mathematical Society (2002) and the Salem Prize (2000).
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Hilbert's Fifth Problem and Related Topics
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American Mathematical Society, 2014
ISBN 10: 147041564X
ISBN 13: 9781470415648
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Hilbert's Fifth Problem and Related Topics (eng)
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Hilbert's Fifth Problem and Related Topics
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Hilbert's Fifth Problem and Related Topics
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Hilbert's fifth problem and related topics. Graduate studies in mathematics; Volume 153.
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Providence, American Mathematical Society, 2014
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Hardcover. xiii, 338 p. Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. C-04829 9781470415648 Sprache: Englisch Gewicht in Gramm: 1150. Seller Inventory # 2491069
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Hilbert's Fifth Problem and Related Topics
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ISBN 10: 147041564X
ISBN 13: 9781470415648
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Hilbert's Fifth Problem and Related Topics
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Hilbert's Fifth Problem and Related Topics
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ISBN 10: 147041564X
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Hilbert's Fifth Problem and Related Topics
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Hardback. Condition: New. Winner of the 2015 Prose Award for Best Mathematics Book!In the fifth of his famous list of 23 problems, Hilbert asked if every topological group which was locally Euclidean was in fact a Lie group. Through the work of Gleason, Montgomery-Zippin, Yamabe, and others, this question was solved affirmatively; more generally, a satisfactory description of the (mesoscopic) structure of locally compact groups was established. Subsequently, this structure theory was used to prove Gromov's theorem on groups of polynomial growth, and more recently in the work of Hrushovski, Breuillard, Green, and the author on the structure of approximate groups.In this graduate text, all of this material is presented in a unified manner, starting with the analytic structural theory of real Lie groups and Lie algebras (emphasising the role of one-parameter groups and the Baker-Campbell-Hausdorff formula), then presenting a proof of the Gleason-Yamabe structure theorem for locally compact groups (emphasising the role of Gleason metrics), from which the solution to Hilbert's fifth problem follows as a corollary. After reviewing some model-theoretic preliminaries (most notably the theory of ultraproducts), the combinatorial applications of the Gleason-Yamabe theorem to approximate groups and groups of polynomial growth are then given. A large number of relevant exercises and other supplementary material are also provided. Seller Inventory # LU-9781470415648
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Hilbert's Fifth Problem and Related Topics
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ISBN 10: 147041564X
ISBN 13: 9781470415648
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