## Ramanujan Complexes of Type Ãd

#### Beth SamuelsYale UniversityMathematics

I will define and construct Ramanujan complexes. These are simplicial complexes which are higher dimensional analogues of Ramanujan graphs. They are obtained as quotients of the buildings of type Ãd - 1 associated with PGLd(F) where F is a local field of positive characteristic.

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