Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scattering diagrams of quivers with potentials and mutations   For a quiver with non-degenerate potential, we study the associated stability
scattering diagram and how it changes under mutations. We show that under
mutations the stability scattering diagram behaves like the cluster scattering
diagram associated to the same quiver, which gives them identical cluster
chamber structures. As an application, we prove if the quiver has a
green-to-red sequence, these two scattering diagrams are identical and if the
quiver comes from a once-punctured torus, they differ by a central
wall-crossing. This verifies in those cases a conjecture of
Kontsevich-Soibelman that a particular set of initial data given by a quiver
determines the Donaldson-Thomas series of the quiver with a non-degenerate
potential.

20
The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an