POSITIVE GRASSMANNIAN AND POLYHEDRAL SUBDIVISIONS by POSTNIKOV, ALEXANDER

“…© ICM 2018.All rights reserved. The nonnegative Grassmannian is a cell complex with rich geometric, algebraic, and combinatorial structures. …”
Get full text

Arrangements of equal minors in the positive Grassmannian by Farber, Miriam, Postnikov, Alexander

“…Weakly separated sets, originally introduced by Leclerc and Zelevinsky, are closely related to the positive Grassmannian and the associated cluster algebra. However, we also construct examples of arrangements of smallest minors which are not weakly separated using chain reactions of mutations of plabic graphs. …”
Get full text
Get full text
Get full text

Mirabolic affine Grassmannian and character sheaves by Ginzburg, Victor, Travkin, Roman, Finkelberg, Michael

Get full text
Get full text

0-Cycles on Grassmannians as Representations of Projective Groups by Bezrukavnikov, R., Rovinsky, M.

Get full text

Parity sheaves on the affine Grassmannian and the Mirković–Vilonen conjecture by Achar, Pramod N., Rider, Laura

“…We prove the Mirković–Vilonen conjecture: the integral local intersection cohomology groups of spherical Schubert varieties on the affine Grassmannian have no p-torsion, as long as p is outside a certain small and explicitly given set of prime numbers. …”
Get full text
Get full text

Arrangements of minors in the positive Grassmannian and a triangulation of the hypersimplex by Farber, Miriam, Mandelshtam, Yelena

“…The structure of zero and nonzero minors in the Grassmannian leads to rich combinatorics of matroids. …”
Get full text
Get full text

Scattering equations: from projective spaces to tropical grassmannians by Cachazo, Freddy, Early, Nick, Guevara, Alfredo, Mizera, Sebastian

“…We compute all ‘biadjoint amplitudes’ for (k, n) = (3, 6) and find a direct connection to the tropical Grassmannian. This leads to the notion of k = 3 Feynman diagrams. …”
Get full text

Positive Configuration Space by Arkani-Hamed, Nima, Lam, Thomas, Spradlin, Marcus

“…Abstract We define and study the totally nonnegative part of the Chow quotient of the Grassmannian, or more simply the nonnegative configuration space. …”
Get full text

Weak separation and plabic graphs by Oh, S., Speyer, D. E., Postnikov, Alexander

“…Postnikov studied total positivity on the Grassmannian. He described a stratification of the totally non-negative Grassmannian into positroid strata, and constructed theirparameterization using plabic graphs. …”
Get full text
Get full text

Moduli spaces of sheaves on surfaces: Hecke correspondences and representation theory by Neguţ, A

“…For example, the moduli space of linear subspaces of 𝔸n is the Grassmannian variety, which is a classical object in representation theory. …”
Get full text

Central extensions by K2 and factorization line bundles by Tao, James, Zhao, Yifei

“…Given a connected, reductive group G, we prove that central extensions of G by the sheaf K2 on the big Zariski site of X, studied in Brylinski–Deligne [5], are equivalent to factorization line bundles on the Beilinson–Drinfeld affine Grassmannian GrG. Our result affirms a conjecture of Gaitsgory–Lysenko [13] and classifies factorization line bundles on GrG. .…”
Get full text

A Fourier transform for the quantum Toda lattice by Lonergan, Gus

“…The proof is contained in Sect. 2 and relies on a result of Bezrukavnikov–Finkelberg realizing the quantum Toda lattice as the equivariant homology of the dual affine Grassmannian; the Fourier transform boils down to nothing more than the duality between homology and cohomology. …”
Get full text

Flip cycles in plabic graphs by Balitskiy, Alexey, Wellman, Julian

“…Abstract Planar bicolored (plabic) graphs are combinatorial objects introduced by Postnikov to give parameterizations of the positroid cells of the totally nonnegative Grassmannian $$\text {Gr}^{\ge 0}(n,k)$$Gr≥0(n,k). Any two plabic graphs for the same positroid cell can be related by a sequence of certain moves. …”
Get full text

Weak Separation, Pure Domains and Cluster Distance by Farber, Miriam, Galashin, Pavel

“…We apply our result to calculate the cluster distance and to give lower bounds on the mutation distance between cluster variables in the cluster algebra structure on the coordinate ring of the Grassmannian. Using a linear projection that relates weak separation to the octahedron recurrence, we also find the exact mutation distances and cluster distances for a family of cluster variables.…”
Get full text

A cluster of results on amplituhedron tiles by Even-Zohar, Chaim, Lakrec, Tsviqa, Parisi, Matteo, Sherman-Bennett, Melissa, Tessler, Ran, Williams, Lauren

“…It generalizes cyclic polytopes and the positive Grassmannian and has a very rich combinatorics with connections to cluster algebras. …”
Get full text

A canonical expansion of the product of two Stanley symmetric functions by Li, Nan

“…In the case when one permutation is Grassmannian, we have a better understanding of this stability. …”
Get full text

Schur Times Schubert via the Fomin-Kirillov Algebra by Meszaros, Karola, Panova, Greta, Postnikov, Alexander

“…We study multiplication of any Schubert polynomial S[subscript w] by a Schur polynomial sλ (the Schubert polynomial of a Grassmannian permutation) and the expansion of this product in the ring of Schubert polynomials. …”
Get full text
Get full text

On-shell structures of MHV amplitudes beyond the planar limit by Arkani-Hamed, Nima, Bourjaily, Jacob L., Cachazo, Freddy, Postnikov, Alexander, Trnka, Jaroslav

“…This is understood in terms of an extended notion of positivity in G(2, n), the Grassmannian of 2-planes in n dimensions: a single on-shell diagram can be associated with many different “positive” regions, of which the familiar G [subscript +](2, n) associated with planar diagrams is just one example. …”
Get full text
Get full text

Stringy canonical forms by Arkani-Hamed, Nima, He, Song, Lam, Thomas

“…We also discuss a number of other examples, including stringy canonical forms for finite-type cluster algebras (with type A corresponding to usual string amplitudes), and other natural integrals over the positive Grassmannian.…”
Get full text

Some remarks concerning Voevodsky’s nilpotence conjecture by Bernardara, Marcello, Marcolli, Matilde, Trigo Neri Tabuada, Goncalo Jorge

“…Making use of this noncommutative generalization, we then address Voevodsky’s original conjecture in the following cases: quadric fibrations, intersection of quadrics, linear sections of Grassmannians, linear sections of determinantal varieties, homological projective duals, and Moishezon manifolds.…”
Get full text
Get full text