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2017

Scattering fans

Reading, Nathan

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Scattering diagrams arose in the context of mirror symmetry, Donaldson-Thomas theory, and integrable systems.

We show that a consistent scattering diagram with minimal support cuts the ambient space into a complete fan.
A special class of scattering diagrams, the cluster scattering diagrams, are closely related to cluster algebras.
We show that the cluster scattering fan associated to an exchange matrix $B$ refines the mutation fan for $B$ (a complete fan that encodes the geometry of mutations of $B$).

Scattering fans · Around

Built on

R. Webster, Convexity
1994
Earlier work this paper cites.
S. Fomin and A. Zelevinsky, Cluster algebras. I. Foundations
2002
Earlier work this paper cites.
A. Berenstein, S. Fomin and A. Zelevinsky, Cluster algebras. III. Upper bounds and double Bruhat cells
2005
Earlier work this paper cites.
S. Fomin and A. Zelevinsky, Cluster Algebras IV: Coefficients
2007
Earlier work this paper cites.
V. V. Fock and A. B. Goncharov, Cluster ensembles, quantization and the dilogarithm
2009
Earlier work this paper cites.

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N. Reading, Universal geometric cluster algebras
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Then

G. Muller, The existence of a maximal green sequence is not invariant under quiver mutation
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2015
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M. W. Cheung, M. Gross, G. Muller, G. Musiker, D. Rupel, S. Stella, and H. Williams, The greedy basis equals the theta basis: a rank two haiku
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M. Gross, P. Hacking, S. Keel, and M. Kontsevich, Canonical bases for cluster algebras
2018
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N. Reading, A combinatorial approach to scattering diagrams
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2018
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