A $t$-generalization for Schubert Representatives of the Affine Grassmannian by Avinash J. Dalal, Jennifer Morse

“…We introduce two families of symmetric functions with an extra parameter $t$ that specialize to Schubert representatives for cohomology and homology of the affine Grassmannian when $t=1$. The families are defined by a statistic on combinatorial objects associated to the type-$A$ affine Weyl group and their transition matrix with Hall-Littlewood polynomials is $t$-positive. …”
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Real Hypersurfaces in Complex Grassmannians of Rank Two by Dehe Li, Shujie Zhai

Subjects: “…complex Grassmannians of rank two…”
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The ABC's of affine Grassmannians and Hall-Littlewood polynomials by Avinash J. Dalal, Jennifer Morse

“…In doing so, we prove a new combinatorial formula for representatives of the Schubert classes for the cohomology of affine Grassmannians. We show how new combinatorics involved in our formulas gives the Kostka-Foulkes polynomials and discuss how this can be applied to study the transition matrices between Hall-Littlewood and $k$-Schur functions.…”
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0-Cycles on Grassmannians as Representations of Projective Groups by Bezrukavnikov, R., Rovinsky, M.

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The Beilinson-Bernstein localization theorem for the affine Grassmannian by Fortuna, Giorgia

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Rational points on Grassmannians and unlikely intersections in tori by Capuano, L, Masser, D, Pila, J, Zannier, U

Gravity in Twistor Space and its Grassmannian Formulation by Cachazo, F, Mason, L, Skinner, D

“…In addition, we provide a description of gravity amplitudes as a multidimensional contour integral over a Grassmannian. The Grassmannian formulation has a very simple structure; in the N$^{k-2}$MHV sector the integrand is essentially the product of that of an MHV and an $\overline{{\rm MHV}}$ amplitude, with $k+1$ and $n-k-1$ particles respectively.…”

Dual Superconformal Invariance, Momentum Twistors and Grassmannians by Mason, L, Skinner, D

“…We show that tree amplitudes and box coefficients are succinctly generated by integration of holomorphic delta-functions in momentum twistors over cycles in a Grassmannian. This is analogous to, although distinct from, recent results obtained by Arkani-Hamed et al. in ordinary twistor space. …”

Arrangements Of Minors In The Positive Grassmannian And a Triangulation of The Hypersimplex by Miriam Farber, Yelena Mandelshtam

“…The structure of zero and nonzero minors in the Grassmannian leads to rich combinatorics of matroids. …”
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Torus quotient of the Grassmannian $G_{n,2n}$ by Nayek, Arpita, Saha, Pinakinath

Subjects: “…Grassmannian…”
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Cohomology algebra of mapping spaces between quaternion Grassmannians by oteng maphane

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Endpoint Geodesic Formulas on Graßmannians Applied to Interpolation Problems by Knut Hüper, Fátima Silva Leite

Subjects: “…Graßmannians…”
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Affine type A geometric crystal structure on the Grassmannian by Gabriel Frieden

“…In particular, the promotion operation on these tableaux essentially corresponds to cyclically shifting the Plu ̈cker coordinates of the Grassmannian.…”
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Composite non-Abelian strings with Grassmannian models on the worldsheet by Edwin Ireson, Mikhail Shifman, Alexei Yung

“…The generalization is straightforward and provides, among other results, a simple and transparent way for counting the number of vacua in N=(2,2) Grassmannian model.…”
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Aerodynamic Shape Optimization with Grassmannian Shape Parameterization Method by Yang Zhang, Bo Pang, Xiankai Li, Gang Chen

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An equivariant rim hook rule for quantum cohomology of Grassmannians by Elizabeth Beazley, Anna Bertiger, Kaisa Taipale

“…Bertram, Ciocan-Fontanine and Fulton provide a way to compute quantum products of Schubert classes in the Grassmannian of $k$-planes in complex $n$-space by doing classical multiplication and then applying a combinatorial rimhook rule which yields the quantum parameter. …”
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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. …”
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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. …”
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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. …”
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Double transitivity of Galois groups in Schubert calculus of Grassmannians by Sottile, Frank, White, Jacob

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