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Discrete Groups, Expanding Graphs and Invariant Measures: Appendix by Jonathan D. Rogawski - Couverture souple
Synopsis
In the last ?fteen years two seemingly unrelated problems, one in computer science and the other in measure theory, were solved by amazingly similar techniques from representation theory and from analytic number theory. One problem is the - plicit construction of expanding graphs («expanders»). These are highly connected sparse graphs whose existence can be easily demonstrated but whose explicit c- struction turns out to be a dif?cult task. Since expanders serve as basic building blocks for various distributed networks, an explicit construction is highly des- able. The other problem is one posed by Ruziewicz about seventy years ago and studied by Banach [Ba]. It asks whether the Lebesgue measure is the only ?nitely additive measure of total measure one, de?ned on the Lebesgue subsets of the n-dimensional sphere and invariant under all rotations. The two problems seem, at ?rst glance, totally unrelated. It is therefore so- what surprising that both problems were solved using similar methods: initially, Kazhdan’s property (T) from representation theory of semi-simple Lie groups was applied in both cases to achieve partial results, and later on, both problems were solved using the (proved) Ramanujan conjecture from the theory of automorphic forms. The fact that representation theory and automorphic forms have anything to do with these problems is a surprise and a hint as well that the two questions are strongly related.
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Présentation de l'éditeur
Unifying concepts from various fields within mathematics, this volume offers solutions to two known problems – the construction of expanding graphs and the Ruziewicz problem, concerning the finitely additive invariant measures of spheres.
Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.
- ÉditeurBirkhäuser
- Date d'édition2009
- ISBN 10 3034603312
- ISBN 13 9783034603317
- ReliureBroché
- Langueanglais
- Numéro d'édition1
- Nombre de pages208
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Discrete Groups, Expanding Graphs and Invariant Measures
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Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Award-winning monograph of the Ferran Sunyer i Balaguer Prize 1993Exciting tour through several areas of mathematicsRecent mathematical researchAward-winning monograph of the Ferran Sunyer i Balaguer Prize 1993Exciting tou. N° de réf. du vendeur 4317923
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Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -In the last fteen years two seemingly unrelated problems, one in computer science and the other in measure theory, were solved by amazingly similar techniques from representation theory and from analytic number theory. One problem is the - plicit construction of expanding graphs ('expanders'). These are highly connected sparse graphs whose existence can be easily demonstrated but whose explicit c- struction turns out to be a dif cult task. Since expanders serve as basic building blocks for various distributed networks, an explicit construction is highly des- able. The other problem is one posed by Ruziewicz about seventy years ago and studied by Banach [Ba]. It asks whether the Lebesgue measure is the only nitely additive measure of total measure one, de ned on the Lebesgue subsets of the n-dimensional sphere and invariant under all rotations. The two problems seem, at rst glance, totally unrelated. It is therefore so- what surprising that both problems were solved using similar methods: initially, Kazhdan's property (T) from representation theory of semi-simple Lie groups was applied in both cases to achieve partial results, and later on, both problems were solved using the (proved) Ramanujan conjecture from the theory of automorphic forms. The fact that representation theory and automorphic forms have anything to do with these problems is a surprise and a hint as well that the two questions are strongly related. 196 pp. Englisch. N° de réf. du vendeur 9783034603317
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Discrete Groups, Expanding Graphs and Invariant Measures : Appendix by Jonathan D. Rogawski
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ISBN 10 : 3034603312
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Taschenbuch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - In the last fteen years two seemingly unrelated problems, one in computer science and the other in measure theory, were solved by amazingly similar techniques from representation theory and from analytic number theory. One problem is the - plicit construction of expanding graphs ('expanders'). These are highly connected sparse graphs whose existence can be easily demonstrated but whose explicit c- struction turns out to be a dif cult task. Since expanders serve as basic building blocks for various distributed networks, an explicit construction is highly des- able. The other problem is one posed by Ruziewicz about seventy years ago and studied by Banach [Ba]. It asks whether the Lebesgue measure is the only nitely additive measure of total measure one, de ned on the Lebesgue subsets of the n-dimensional sphere and invariant under all rotations. The two problems seem, at rst glance, totally unrelated. It is therefore so- what surprising that both problems were solved using similar methods: initially, Kazhdan's property (T) from representation theory of semi-simple Lie groups was applied in both cases to achieve partial results, and later on, both problems were solved using the (proved) Ramanujan conjecture from the theory of automorphic forms. The fact that representation theory and automorphic forms have anything to do with these problems is a surprise and a hint as well that the two questions are strongly related. N° de réf. du vendeur 9783034603317
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