Ramanujan graph

Ramanujan graph

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Naser Sardari, Princeton University
Fine Hall 314

We discuss the geometry and spectral properties of expander graphs. We'll define Ramanujan graphs and show why they are optimal "expander graphs". Next, we'll explain the construction of explicit Ramanujan graphs by Lubotzky, Phillips, and Sarnak, and relate geometric and spectral properties of LPS Ramanujan graphs to well-known facts in number theory.