5 problems

Schechtman's sparsification conjecture. Is there a universal constant $C$ such that there is a zonotope $\widetilde Z$ generated by at most

Let $\mathcal S \subseteq 2^{[m]}$ be a set system, let $w:[m]\rightarrow\mathbb{R}_{\geq 0}$ be weights, and let $\epsilon>0$. Write $\operatorname{CL}(\mathcal S)$ for the chain…

Khanna–Putterman–Sudan conjecture. For their notion of CSP sparsifiability, the dependence on the number of variables is always a polynomial with an integral exponent.

Column-threshold sparsification conjecture. Because this dropping strategy is local to each column, the column-threshold approach should better capture the underlying system's beha…

Let $Q$ be a sparsification of a probability distribution $p$, and consider permutation-invariant divergences between $Q$ and $p$. The relevant efficiency result is known for nonne…