Twistor-Strings, Grassmannians and Leading Singularities by Bullimore, M, Mason, L, Skinner, D

“…We go on to show that the genus g twistor-string moduli space for g-loop N^{k-2}MHV amplitudes may be mapped into the Grassmannian G(k,n). Restricting to a leading singularity, the image of this map is a 2(n-2)-dimensional subcycle of G(k,n) of exactly the type found from the Grassmannian residue formula of Arkani-Hamed, Cachazo, Cheung and Kaplan. …”

Twistor-strings, Grassmannians and leading singularities by Bullimore, M, Mason, L, Skinner, D

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. …”

Efficiently computing torus charts in landau-Ginzburg models of complete intersections in Grassmannians of planes by Prince, T

“…In this note, companion to the paper [10], we describe an alternative method for finding Laurent polynomials mirror-dual to complete intersections in Grassmannians of planes, in the sense discussed in [10]. …”

On spaces of maps from Riemann surfaces to Grassmannians and applications to the cohomology of moduli of vector bundles by Kirwan, F

Combinatorial aspects of scattering amplitudes: amplituhedra, T-duality, and cluster algebras by Parisi, M

Subjects: “…Scattering Amplitudes, N=4 Super Yang-Mills Theory, On-shell Methods, Grassmannians, Amplituhedron, Positive Geometries, Algebraic Combinatorics, Combinatorial Algebraic Geometry, Matroid and Positroid Theory, Tropical Geometry, and Cluster Algebras.…”

THE LANDAU-LIFSHITZ EQUATION, ELLIPTIC-CURVES AND THE WARD TRANSFORM by Carey, A, Hannabuss, K, Mason, L, Singer, M

“…An appendix is devoted to a careful definition of the Grassmannian of the Frechet space C∞(S1). © 1993 Springer-Verlag.…”

Tree-level recursion relation and dual superconformal symmetry of the ABJM theory by Gang, D, Huang, Y, Koh, E, Lee, S, Lipstein, A

“…Furthermore, we use the recursion relation to compute six-point and eight-point component amplitudes and match them with independent computations based on Feynman diagrams or the Grassmannian integral formula. As an application of the recursion relation, we prove that all tree-level amplitudes of the ABJM theory have dual superconformal symmetry. …”

Tau functions and the twistor theory of integrable systems by Mason, L, Singer, M, Woodhouse, N

“…We first define τ-functions as generalized cross-ratios of four points on a finite- or infinite-dimensional Grassmannian. We show how this definition can be used to construct a natural flat connection on a determinant line bundle associated with two equivariant holomorphic vector bundles over a twistor space, provided that the action of the symmetries on the bundles has the same normal form at the fixed points for the two bundles. …”

Tree-level Recursion Relation and Dual Superconformal Symmetry of the ABJM Theory by Gang, D, Huang, Y, Koh, E, Lee, S, Lipstein, A

“…Furthermore, we use the recursion relation to compute six-point and eight-point component amplitudes and match them with independent computations based on Feynman diagrams or the Grassmannian integral formula. As an application of the recursion relation, we prove that all tree-level amplitudes of the ABJM theory have dual superconformal symmetry. …”

The correlahedron by Eden, B, Heslop, P, Mason, L

“…Re-expressing the Grassmann dependence of correlation functions of n chiral stress-energy multiplets with Grassmann degree 4k in terms of 4(n + k)-linear bosonic variables, the resulting expressions have an interpretation as volume forms on a Gr(n+k, 4+n+k) Grassmannian, analogous to the expressions for planar amplitudes via the amplituhedron. …”

Perverse coherent sheaves and algebraic K-theory of Kac-Moody flag varieties by Zielinski, T

“…In chapter 4, we study a conjecture of Cautis and Williams describing the equivariant K-theory of the affine Grassmannian. More specifically, we prove a special case of their conjecture in rank 1 by an explicit computation, and provide a strategy for a proof in type A. …”

Scattering Amplitudes and Wilson Loops in Twistor Space by Adamo, T, Bullimore, M, Mason, L, Skinner, D

“…We give a brief review of other ideas in connection with amplitudes in twistor space: twistor-strings, recursion in twistor space, the Grassmannian residue formula for leading singularities and amplitudes as polytopes. …”

Exotic t-structures and actions of quantum affine algebras by Cautis, S, Koppensteiner, C

“…Our main application is to obtain exotic t-structures on certain convolution varieties defined using the Beilinson--Drinfeld and affine Grassmannians. These varieties play an important role in the geometric Langlands program, knot homology constructions, K-theoretic geometric Satake and the coherent Satake category. …”

Spectral networks, abelianization, and opers by Kidwai, O

“…In the final chapter we include some partial results the author has obtained on the existence and uniqueness of abelianizations for certain classes of networks related to Grassmannians.</p>…”

Projective fibrations in weighted scrolls by Mboya, G

“…We initiate the study of fibrations embedded in families of key varieties such as weighted Grassmannians fibrations, leaving detailed investigations for later work.…”

The multidimensional cube recurrence by Henriques, A, Speyer, D

“…We recognize a special case of the multidimensional cube recurrence as giving explicit equations for the isotropic Grassmannians <math><mi is="true" mathvariant="normal">IG</mi><mo is="true" stretchy="false">(</mo><mi is="true">n</mi><mo is="true">−</mo><mn is="true">1</mn><mo is="true">,</mo><mn is="true">2</mn><mi is="true">n</mi><mo is="true" stretchy="false">)</mo></math>. …”