## Biregular expanders and the Ramanujan Conjecture

#### Cristina BallantineCollege of the Holy CrossMathematics

The relationship between regular expander graphs and the Ramanujan Conjecture is well understood and has lead to the definition and construction of asymptotically optimal regular expanders called Ramanujan graphs. In this talk we will show that biregular bipartite graphs obtained from the Bruhat-Tits building of a group whose representations satisfy the Ramanujan conjecture are indeed Ramanujan bigraphs.

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