33 citations · 284 across the 37 of their papers we have counts for
42 papers
Amplituhedra and origami, II: loop level
Pavel Galashin
Building on the recently discovered origami-amplituhedron correspondence, we prove that the BCFW (Britto-Cachazo-Feng-Witten) cells triangulate the amplituhedron in full gene…
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…
Amplituhedra and origami, I: tree level
Pavel Galashin
We establish a precise correspondence between points of the tree momentum amplituhedron and origami crease patterns. As an application, we prove that the BCFW (Britto-Cachazo…
Monotone links in DAHA and EHA
Pavel Galashin, Thomas Lam
We define monotone links on a torus, obtained as projections of curves in the plane whose coordinates are monotone increasing. Using the work of Morton-Samuelson, to each monotone…
Braid variety cluster structures, II: general type
Pavel Galashin, Thomas Lam, Melissa Sherman-Bennett
We show that braid varieties for any complex simple algebraic group are cluster varieties. This includes open Richardson varieties inside the flag variety .
Move-reduced graphs on a torus
Pavel Galashin, Terrence George
We determine which bipartite graphs embedded in a torus are move-reduced. In addition, we classify equivalence classes of such move-reduced graphs under square/spider moves. This e…
Braid variety cluster structures, I: 3D plabic graphs
Pavel Galashin, Thomas Lam, Melissa Sherman-Bennett +1
We introduce -dimensional generalizations of Postnikov's plabic graphs and use them to establish cluster structures for type braid varieties. Our results include known clust…
Plabic links, quivers, and skein relations
Pavel Galashin, Thomas Lam
We study relations between cluster algebra invariants and link invariants. First, we show that several constructions of positroid links (permutation links, Richardson links, grid d…
Rational Noncrossing Coxeter-Catalan Combinatorics
Pavel Galashin, Thomas Lam, Minh-Tâm Quang Trinh +1
We solve two open problems in Coxeter-Catalan combinatorics. First, we introduce a family of rational noncrossing objects for any finite Coxeter group, using the combinatorics of d…
The twist for Richardson varieties
Pavel Galashin, Thomas Lam
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 posit…
Totally nonnegative critical varieties
Pavel Galashin
We study totally nonnegative parts of critical varieties in the Grassmannian. We show that each totally nonnegative critical variety Crit is the image of an affine poset…
-associahedra
Pavel Galashin
For each poset , we construct a polytope called the -associahedron. Similarly to the case of graph associahedra, the faces of correspond to certain nested colle…
Positroid Catalan numbers
Pavel Galashin, Thomas Lam
Given a permutation , we study the positroid Catalan number defined to be the torus-equivariant Euler characteristic of the associated open positroid variety. We introduce…
Critical varieties in the Grassmannian
Pavel Galashin
We introduce a family of spaces called critical varieties. Each critical variety is a subset of one of the positroid varieties in the Grassmannian. The combinatorics of positroid v…
Positroids, knots, and -Catalan numbers
Pavel Galashin, Thomas Lam
We relate the mixed Hodge structure on the cohomology of open positroid varieties (in particular, their Betti numbers over and point counts over ) to Kho…
A formula for boundary correlations of the critical Ising model
Pavel Galashin
Given a finite rhombus tiling of a polygonal region in the plane, the associated critical -invariant Ising model is invariant under star-triangle transformations. We give a simp…
Symmetries of stochastic colored vertex models
Pavel Galashin
We discover a new property of the stochastic colored six-vertex model called flip-invariance. We use it to show that for a given collection of observables of the model, any transfo…
Higher secondary polytopes and regular plabic graphs
Pavel Galashin, Alexander Postnikov, Lauren Williams
Given a configuration of points in , we introduce the higher secondary polytopes , which have the property that agrees…
Positroid varieties and cluster algebras
Pavel Galashin, Thomas Lam
We show that the coordinate ring of an open positroid variety coincides with the cluster algebra associated to a Postnikov diagram. This confirms conjectures of Postnikov, Muller--…
Regularity theorem for totally nonnegative flag varieties
Pavel Galashin, Steven N. Karp, Thomas Lam
We show that the totally nonnegative part of a partial flag variety (in the sense of Lusztig) is a regular CW complex, confirming a conjecture of Williams. In particular, the…
Ising model and the positive orthogonal Grassmannian
Pavel Galashin, Pavlo Pylyavskyy
We completely describe by inequalities the set of boundary correlation matrices of planar Ising networks embedded in a disk. Specifically, we build on a recent result of M.~Lis to…
Some more amplituhedra are contractible
Pavle V. M. Blagojević, Pavel Galashin, Nevena Palić +1
The amplituhedra arise as images of the totally nonnegative Grassmannians by projections that are induced by linear maps. They were introduced in Physics by Arkani-Hamed \& Trnka (…
Parity duality for the amplituhedron
Pavel Galashin, Thomas Lam
The (tree) amplituhedron is a certain subset of the Grassmannian introduced by Arkani-Hamed and Trnka in 2013 in order to study scattering amplitudes in $N=…
Trianguloids and Triangulations of Root Polytopes
Pavel Galashin, Gleb Nenashev, Alexander Postnikov
Triangulations of a product of two simplices and, more generally, of root polytopes are closely related to Gelfand-Kapranov-Zelevinsky's theory of discriminants, to tropical geomet…