Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inverse Problems in Topological Persistence   In this survey, we review the literature on inverse problems in topological
persistence theory. The first half of the survey is concerned with the question
of surjectivity, i.e. the existence of right inverses, and the second half
focuses on injectivity, i.e. left inverses. Throughout, we highlight the tools
and theorems that underlie these advances, and direct the reader's attention to
open problems, both theoretical and applied.

19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
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The categories of this paper are: solv-int
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol