Expanders, Ramanujan graphs and random lifts

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• Benny Sudakov (UCLA)
• Wednesday 10 March 2010, 14:30-15:30
• MR12.

If you have a question about this talk, please contact Andrew Thomason.

Expansion of a graph is one of the most fundamental concepts in modern combinatorics, which has numerous applications in many mathematical areas. It is well known that expansion is closely relates to the spectral properties 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 graphs that meet this bound are called Ramanujan Graphs. There are still many unresolved questions about the existence of such graphs. In this talk we survey this background material, then we explain what lifts of graphs are and how the above questions can be approached using random lifts of graphs.

Joint work with Lubetzky and Vu.

This talk is part of the Combinatorics Seminar series.

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