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In cite{FGLNP}, Fox, Gromov, Lafforgue, Naor and Pach, in a respond to a question of Gromov cite{G}, constructed bounded degree geometric expanders, namely, simplical complexes having the affine overlapping property. Their explicit constructions are finite quotients of $tilde{A_d}$-buildings, for $dgeq 2$, over local fields. In this paper, this result is extended to general high rank Bruhat-Tits buildings.
Given a split semisimple group over a local field, we consider the maximal Satake-Berkovich compactification of the corresponding Euclidean building. We prove that it can be equivariantly identified with the compactification which we get by embedding
Given a semisimple group over a complete non-Archimedean field, it is well known that techniques from non-Archimedean analytic geometry provide an embedding of the corresponding Bruhat-Tits builidng into the analytic space associated to the group; by
Let K be a function field with constant field k and let infinity be a fixed place of K. Let C be the Dedekind domain consisting of all those elements of K which are integral outside infinity. The group G=GL_2(C) is important for a number of reasons.
We apply the theory of fundamental strata of Bremer and Sage to find cohomologically rigid $G$-connections on the projective line, generalising the work of Frenkel and Gross. In this theory, one studies the leading term of a formal connection with re
A two-dimensional simplicial complex is called $d$-{em regular} if every edge of it is contained in exactly $d$ distinct triangles. It is called $epsilon$-expanding if its up-down two-dimensional random walk has a normalized maximal eigenvalue which