Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectra of biperiodic planar networks   A biperiodic planar network is a pair $(G,c)$ where $G$ is a graph embedded
on the torus and $c$ is a function from the edges of $G$ to non-zero complex
numbers. Associated to the discrete Laplacian on a biperiodic planar network is
its spectrum: a triple $(C,S,\nu)$, where $C$ is a curve and $S$ is a divisor
on it. We give a complete classification of networks (modulo a natural
equivalence) in terms of their spectral data. The space of networks has a large
group of cluster automorphisms arising from the $Y-\Delta$ transformations. We
show that the spectrum provides action-angle coordinates for the discrete
cluster integrable systems defined by these automorphisms.

36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio