If you have any questions, you are always welcome to contact us. We'll get back to you as soon as possible, withing 24 hours on weekdays.
Customer service
All questions about your order, return and delivery must be sent to our customer service team by e-mail at yourstore@yourdomain.com
Sale & Press
If you are interested in selling our products, need more information about our brand or wish to make a collaboration, please contact us at press@yourdomain.com
Help
If you have any questions, you are always welcome to contact us. We'll get back to you as soon as possible, withing 24 hours on weekdays.
Customer service
All questions about your order, return and delivery must be sent to our customer service team by e-mail at yourstore@yourdomain.com
Sale & Press
If you are interested in selling our products, need more information about our brand or wish to make a collaboration, please contact us at press@yourdomain.com
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 ndimensional 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, Kazhdans property (T) from representation theory of semisimple 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.
⚠️ WARNING (California Proposition 65):
This product may contain chemicals known to the State of California to cause cancer,
birth defects, or other reproductive harm.
For MAP (Minimum Advertised Price) violations and Intellectual Property (IP) or Trademark concerns, please contact:
support@ergodebooks.com
⚠️ California Proposition 65 Warning: Some products sold on this website may expose you to chemicals known to the State of California to cause cancer, birth defects, or other reproductive harm. For more information, visit www.P65Warnings.ca.gov.
