Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isogeny graphs on superspecial abelian varieties: Eigenvalues and
  Connection to Bruhat-Tits buildings   We study for each fixed integer $g \ge 2$, for all primes $\ell$ and $p$ with
$\ell \neq p$, finite regular directed graphs associated with the set of
equivalence classes of $\ell$-marked principally polarized superspecial abelian
varieties of dimension $g$ in characteristic $p$, and show that the adjacency
matrices have real eigenvalues with spectral gaps independent of $p$. This
implies a rapid mixing property of natural random walks on the family of
isogeny graphs beyond the elliptic curve case and suggests a potential
construction of the Charles-Goren-Lauter type cryptographic hash functions for
abelian varieties. We give explicit lower bounds for the gaps in terms of the
Kazhdan constant for the symplectic group when $g \ge 2$, and discuss optimal
values in view of the theory of automorphic representations when $g=2$. As a
by-product, we also show that the finite regular directed graphs constructed by
Jordan-Zaytman also has the same property.

21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th