5 problems

Modular collapse conjecture. The cocycle collapses:

Let $\mathbb{X}$ be a unimodular topological group, and let $\mathfrak{m}$ be a flow-adapted simple point process on $\mathbb{X}$. The point process is connectible in a flow-adapte…

A unimodular graph is a random rooted graph satisfying the mass-transport principle, and a Benjamini–Schramm limit is a local weak limit of finite graphs. Unimodular graph finite-m…

A graphing is a bounded-degree Borel graph satisfying the Intrinsic Mass Transport Principle. A bounded-degree graph sequence has a Benjamini–Schramm limit when the distribution of…

Aldous–Lyons conjecture. Every involution-invariant measure on $\mathfrak{G}$ arises as a graph limit.