Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Automorphisms and isogeny graphs of abelian varieties, with applications
  to the superspecial Richelot isogeny graph   We investigate special structures due to automorphisms in isogeny graphs of
principally polarized abelian varieties, and abelian surfaces in particular. We
give theoretical and experimental results on the spectral and statistical
properties of (2, 2)-isogeny graphs of superspecial abelian surfaces, including
stationary distributions for random walks, bounds on eigenvalues and diameters,
and a proof of the connectivity of the Jacobian subgraph of the (2, 2)-isogeny
graph. Our results improve our understanding of the performance and security of
some recently-proposed cryptosystems, and are also a concrete step towards a
better understanding of general superspecial isogeny graphs in arbitrary
dimension.

28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ