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SUMMARY:Expanders\, Ramanujan graphs and random lifts - Benny Sudakov (UCL
 A)
DTSTART:20100310T143000Z
DTEND:20100310T153000Z
UID:TALK23262@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:Expansion of a graph is one of the most fundamental concepts i
 n modern combinatorics\, which has numerous applications in many mathemati
 cal areas. It is well known that expansion is closely relates to the spect
 ral\nproperties of graph. The celebrated Alon-Boppana bound says that all 
 eigenvalues of a d-regular graph must be at least 2sqrt(d-1) - o(1) and gr
 aphs that meet this bound are called Ramanujan Graphs. There are still\nma
 ny unresolved questions about the existence of such graphs. In this talk w
 e survey this background material\, then we explain what lifts of graphs a
 re and how the above questions can be approached using random lifts of gra
 phs.\n\nJoint work with Lubetzky and Vu.\n
LOCATION:MR12
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