discrete groups expanding graphs di lubotzky alex (11 risultati)

8° , Hardcover/Pappeinband. 1.Auflage,. xi, 195 Seiten Einband etwas berieben, Bibl.Ex., innen guter und sauberer Zustand 9783764350758 Sprache: Englisch Gewicht in Gramm: 481.

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Taschenbuch. Condizione: 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.

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Condizione: 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.

Taschenbuch. Condizione: 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.

Condizione: New. Print on Demand pp. 206 49:B&W 6.14 x 9.21 in or 234 x 156 mm (Royal 8vo) Perfect Bound on White w/Gloss Lam.

Condizione: New. PRINT ON DEMAND pp. 206.