Extriangulated categories axiomatise extension-closed subcategories of triangulated
categories and generalise both exact categories and triangulated categories. This survey …

A bstract Canonical forms of positive geometries play an important role in revealing hidden
structures of scattering amplitudes, from amplituhedra to associahedra. In this paper, we …

A bstract The “amplituhedron” for tree-level scattering amplitudes in the bi-adjoint ϕ 3 theory
is given by the ABHY associahedron in kinematic space, which has been generalized to …

We show that the mesh mutations are the minimal relations among the gg‐vectors with
respect to any initial seed in any finite‐type cluster algebra. We then use this algebraic result …

For each Dynkin diagram $ D $, we define a''cluster configuration space''${\mathcal {M}} _D
$ and a partial compactification ${\widetilde {\mathcal {M}}} _D $. For $ D= A_ {n-3} $, we …

This review is a primer on recently established geometric methods for observables in
quantum field theories. The main emphasis is on amplituhedra, ie geometries encoding …

A bstract In [1], two of the present authors along with P. Raman attempted to extend the
Amplituhedron program for scalar field theories [2] to quartic scalar interactions. In this paper …

For a finite dimensional algebra $ A $ over a field $ k $, the 2-term silting complexes of $ A $
gives a simplicial complex $\Delta (A) $ called the\emph {$ g $-simplicial complex}. We give …

A bstract In this paper, we present new expressions for n-point NMHV tree-level gravity
amplitudes. We introduce a method of factorization diagrams which is a simple graphical …

A bstract We continue the study of positive geometries underlying the Grassmannian string
integrals, which are a class of “stringy canonical forms”, or stringy integrals, over the positive …