Abstract Birational toggling on Gelfand–Tsetlin patterns appeared first in the study of
geometric crystals and geometric Robinson–Schensted–Knuth correspondence. Based on …

We construct the twist automorphism of open Richardson varieties inside the flag variety of a
complex semisimple algebraic group. We show that the twist map preserves totally positive …

Given one of an infinite class of supersymmetric quiver gauge theories, string theorists can
associate a corresponding toric variety (which is a Calabi–Yau 3-fold) as well as an …

We show that Zamolodchikov dynamics of a recurrent quiver has zero algebraic entropy only
if the quiver has a weakly subadditive labeling, and conjecture the converse. By assigning a …

We review several constructions of integrable systems with an underlying cluster algebra
structure, in particular the Gekhtman-Shapiro-Tabachnikov-Vainshtein construction based …

Strictly subadditive, subadditive and weakly subadditive labelings of quivers were
introduced by the second author, generalizing Vinberg's definition for undirected graphs. In …

We introduce a new method for producing both maximal green and reddening sequences of
quivers. The method, called component preserving mutations, generalizes the notion of …

We classify periodic Y-systems of rank 2 satisfying the symplectic property. We find that there
are six such Y-systems. In all cases, the periodicity follows from the existence of two …

We characterize Y/T-system-type difference equations arising from cluster algebras by
triples of matrices, which we call T-data, that have a certain symplectic property. We show …

We prove a general theorem that gives a linear recurrence for tuples of paths in every
cylindrical network. This can be seen as a cylindrical analog of the Lindström–Gessel …