Zobrazeno 1 - 10
of 138
pro vyhledávání: '"Galashin, Pavel"'
Autor:
Galashin, Pavel
We establish a precise correspondence between points of momentum amplituhedra and origami crease patterns. As an application, we prove that the BCFW cells triangulate the momentum amplituhedron when all Mandelstam variables are nonnegative. As anothe
Externí odkaz:
http://arxiv.org/abs/2410.09574
Autor:
Galashin, Pavel, Lam, Thomas
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 link we associate elements in the double affine Hecke algebra and the
Externí odkaz:
http://arxiv.org/abs/2307.16794
We show that braid varieties for any complex simple algebraic group $G$ are cluster varieties. This includes open Richardson varieties inside the flag variety $G/B$.
Comment: 29 pages. v2: minor changes
Comment: 29 pages. v2: minor changes
Externí odkaz:
http://arxiv.org/abs/2301.07268
Autor:
Galashin, Pavel, George, Terrence
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 extends the class of minimal graphs on a torus studied by Goncharov-Ken
Externí odkaz:
http://arxiv.org/abs/2212.12962
We introduce $3$-dimensional generalizations of Postnikov's plabic graphs and use them to establish cluster structures for type $A$ braid varieties. Our results include known cluster structures on open positroid varieties and double Bruhat cells, and
Externí odkaz:
http://arxiv.org/abs/2210.04778
Autor:
Galashin, Pavel, Lam, Thomas
We study relations between cluster algebra invariants and link invariants. First, we show that several constructions of positroid links (permutation links, Richardson links, grid diagram links, plabic graph links) give rise to isotopic links. For a s
Externí odkaz:
http://arxiv.org/abs/2208.01175
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 distinguished subwords. Second, we give a type-uniform proof that these
Externí odkaz:
http://arxiv.org/abs/2208.00121
Autor:
Galashin, Pavel, Lam, Thomas
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 parts, and prove a Chamber Ansatz formula for it. Our twist map ge
Externí odkaz:
http://arxiv.org/abs/2204.05935
Autor:
Galashin, Pavel
We study totally nonnegative parts of critical varieties in the Grassmannian. We show that each totally nonnegative critical variety Crit$^{\ge0}_f$ is the image of an affine poset cyclohedron under a continuous map and use this map to define a bound
Externí odkaz:
http://arxiv.org/abs/2110.08548
Autor:
Galashin, Pavel
For each poset $P$, we construct a polytope $A(P)$ called the $P$-associahedron. Similarly to the case of graph associahedra, the faces of $A(P)$ correspond to certain nested collections of subsets of $P$. The Stasheff associahedron is a compactifica
Externí odkaz:
http://arxiv.org/abs/2110.07257