Discrete Groups, Expanding Graphs and Invariant Measures (Paperback, 1st ed. 1994. 2nd printing 2009)

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."

General

Imprint:	Birkhauser Verlag AG
Country of origin:	Switzerland
Series:	Modern Birkhauser Classics
Release date:	November 2009
First published:	1994
Appendix by:	Jonathan D. Rogawski
Authors:	Alex Lubotzky
Dimensions:	235 x 155 x 12mm (L x W x T)
Format:	Paperback
Pages:	196
Edition:	1st ed. 1994. 2nd printing 2009
ISBN-13:	978-3-03-460331-7
Categories:	Books > Science & Mathematics > Mathematics > Algebra > Groups & group theory Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Real analysis Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry Books > Science & Mathematics > Mathematics > Number theory > General Promotions
LSN:	3-03-460331-2
Barcode:	9783034603317

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