3 problems

Transversal-representative conjecture. For any $[({u,v},{w})]\in\hat{\mathcal{U}}$, there exists $(u_1',\ldots,u_{m+1}',{w'})\in[({u,v},{w})]$ such that

Transversal intersection conjecture. Schubert varieties of appropriate dimensions intersect transversally after suitable translations by Weyl group elements. This includes the comp…

Let $m$ and $d$ be integers with $0\leq m\leq d-1$, let $r_0,\ldots,r_m\geq 1$ be integers, and set … For sets $X_0,\ldots,X_m\subset\mathbb{R}^d$ with…