We show the existence of cluster $\mathcal {A} $-structures and cluster Poisson structures
on any braid variety, for any simple Lie group. The construction is achieved via weave …

In this manuscript we study braid varieties, a class of affine algebraic varieties associated to
positive braids. Several geometric constructions are presented, including certain torus …

We study braid varieties and their relation to open positroid varieties. We discuss four
different types of braids associated to open positroid strata and show that their associated …

For a finite-dimensional simple Lie algebra g admitting a non-trivial minuscule
representation and a connected marked surface Σ with at least two marked points and no …

We introduce a new operad-like structure that we call a reconnectad; the``input''of an
element of a reconnectad is a finite simple graph, rather than a finite set …

These notes cover the lectures of the first named author at 2021 IHES Summer School on
“Enumerative Geometry, Physics and Representation Theory” with additional details and …

We introduce and study several new topological operads that should be regarded as
nonsymmetric analogues of the operads of little 2‐discs, framed little 2‐discs, and Deligne …

This is a survey article on Richardson varieties and their combinatorics. A Richardson
variety is the intersection, inside the flag manifold GL_n/B_+, of a Schubert cell (B_-u …

We introduce the notion of a polyptych lattice, which encodes a collection of lattices related
by piecewise linear bijections. We initiate a study of the new theory of convex geometry and …

A famous theorem in polytope theory states that the combinatorial type of a simplicial
polytope is completely determined by its facet-ridge graph. This celebrated result was …