Alex Lubotzky

(Author)

Discrete Groups, Expanding Graphs and Invariant Measures (1994. 2nd Printing 2009)Paperback - 1994. 2nd Printing 2009, 23 November 2009

Discrete Groups, Expanding Graphs and Invariant Measures (1994. 2nd Printing 2009)
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Part of Series
Modern Birkhäuser Classics
Print Length
196 pages
Language
English
Publisher
Birkhauser
Date Published
23 Nov 2009
ISBN-10
3034603312
ISBN-13
9783034603317

Description

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.

Product Details

Author:
Alex Lubotzky
Book Edition:
1994. 2nd Printing 2009
Book Format:
Paperback
Country of Origin:
NL
Date Published:
23 November 2009
Dimensions:
23.39 x 15.6 x 1.12 cm
ISBN-10:
3034603312
ISBN-13:
9783034603317
Language:
English
Location:
Basel
Pages:
196
Publisher:
Weight:
294.83 gm

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