Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Flat surfaces and stability structures   We identify spaces of half-translation surfaces, equivalently complex curves
with quadratic differential, with spaces of stability structures on Fukaya-type
categories of punctured surfaces. This is achieved by new methods involving the
complete classification of objects in these categories, which are defined in an
elementary way. We also introduce a number of tools to deal with surfaces of
infinite area, where structures similar to those in cluster algebra appear.

32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th