Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gluing theory of Riemann surfaces and Liouville conformal field theory   We study the gluing theory of Riemann surfaces using formal algebraic
geometry, and give computable relations between the associated parameters for
different gluing processes. As its application to the Liouville conformal field
theory, we construct the sheaf of tempered conformal blocks on the moduli space
of pointed Riemann surfaces which satisfies the factorization property and has
a natural action of the Teichm\"{u}ller groupoid.

37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph