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Geometric Group Theory

GeoGT Session #2.2

Subevent of GeoGT Session #2

Heritage Hall Building 125

Times: 2026 Mar 11 from 04:05PM to 04:25PM (Central Time (US & Canada))

Quasi-isometric embeddings of Ramanujan complexes

Hyein Choi <hc71@rice.edu>, Rice University

Abstract:

Euclidean buildings (a.k.a. affine buildings and Bruhat-Tits buildings) are considered as a p-adic analogue of symmetric spaces. We show that there is no quasi-isometric embedding between the symmetric space of SL(n,R) and the Euclidean building of SL(n,Q_p). Generalizing this, we distinguish Ramanujan complexes constructed by Lubotzky-Samuels-Vishne as finite quotients of Euclidean buildings of PGL(n,F_p((y))) up to quasi-isometric embeddings. These complexes serve as high dimensional expanders with fruitful applications in mathematics and computer science.

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