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Office: Room 2605,
Department of Mathematics,
Shanghai Jiao Tong University
Mail: xiaodong@sjtu.edu.cn
MailingAddress: No.800,
Dong Chuan Road, Shanghai, P.C: 200240
Telephone: 547431482605 
Most important properties of a graph are related to its eigenvalues. However, it is only recently that it has been possible to make this connection precise. New techniques have been developed to control many graph invariants in terms of eigenvalues and eigenfunctions. In particular, this involves a strong twoway interaction between concepts and methods from continuous mathematics and their emerging discrete counterparts. The Neumann eigenvalues are useful for dealing with random walk problems. Thus the eigenvalue lower bounds can be used to bound the rate of convergence of the random walks and polynomial approximation algorithms can be derived for these problems. 
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