3 problems

Broken circuit local-expansion conjecture. For any matroid $M$ of rank $r$ and any ordering $\mathcal{O}$, the broken circuit complex of $M$ is a $(\gamma_0,\dots,\gamma_{r-2})$-lo…

Coboundary expansion conjecture for random balanced Cayley complexes. For any fixed $k\geq 1$ there exist constants $C(k)<\infty$ and $\epsilon(k)>0$ such that for any group $G$, t…

Let the underlying object be a locally spectral expanding structure, such as a simplicial complex or a more general ranked poset, and consider hypercontractivity beyond the second…