9 papers
Cluster tori over , hexagonal moves on triangulations, and minimal coverings of cluster manifolds
Daniel Pérez Melesio, José Simental
We study cluster algebras over . By the Laurent phenomenon there is a map from the set of seeds of the cluster algebra to the corresponding cluster variety. We show t…
Mysterious points in keys but not trees
Scott Neville, José Simental
The deep locus of a cluster variety is defined to be the set of its points that do not belong to any cluster torus. We show that, if the cluster variety has a seed whose mutable pa…
Smooth correspondences between quiver varieties
Nicolle González, Eugene Gorsky, José Simental
We introduce a new class of smooth correspondences between Nakajima quiver varieties called split parabolic quiver varieties, and study their properties. We use these correspondenc…
Positroid Links and Braid varieties
Roger Casals, Eugene Gorsky, Mikhail Gorsky +1
We study braid varieties and their relation to open positroid varieties. We discuss four different types of braids associated to open positroid strata and show that their associate…
Bruhat intervals that are large hypercubes
Jordan Ellenberg, Nicolas Libedinsky, David Plaza +2
We study the question of finding big Bruhat intervals that are poset hypercubes in the symmetric group . Using permutations suggested by AlphaEvolve (an evolutionary coding ag…
Comparing cluster algebras on braid varieties
Roger Casals, Pavel Galashin, Mikhail Gorsky +3
Braid varieties parametrize linear configurations of flags with transversality conditions dictated by positive braids. They include and generalize reduced double Bruhat cells, posi…