Department of Mathematics Calendar
Nathan Reading, NC State, To scatter or to cluster?
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Scattering diagrams arose in the algebraic-geometric theory of mirror symmetry. Recently, Gross, Hacking, Keel, and Kontsevich applied scattering diagrams to prove many longstanding conjectures about cluster algebras. Scattering diagrams are certain collections of codimension-1 cones, each weighted with a formal power series. In this talk, I will introduce cluster scattering diagrams and their connection to cluster algebras, focusing on rank-2 (i.e. 2-dimensional) examples. Even 2-dimensional cluster scattering diagrams are not well-understood in general. I will show how the two-dimensional “affine-type” cases can be constructed using cluster algebras and describe a surprising appearance of the Narayana numbers in the two-dimensional affine case. If time allows, I will discuss a general proof that consistent scattering diagrams cut space into a fan.