7 problems

Let $\mathcal{G}$ be a second countable amenable locally compact Hausdorff groupoid, and let $\Sigma_\nu$ be a Fell line bundle over $\mathcal{G}$. For an element $g\in G$, write…

Let $G$ be a groupoid, let $G'$ denote its isotropy subgroupoid, and let $S$ be an open subgroupoid of $G'$ such that the associated twist restriction $\mathcal{E}_S$ is abelian. P…

Self-binding and scattering conjecture. Any self-bound dynamics of $N$ fermions can be generated from the bi-equivariant groupoid algebra $C^*_{r,\mathcal S_N}(\mathcal G_N)$, whil…

Let ${\rm GICAR}$ denote the groupoid $C^*$-algebra framework for fermionic observables, and let ${\mathcal G}_N$ be the groupoids associated with the $N$-particle sectors. Their m…

Sierakowski's conjecture. If the action of $\Gamma$ on $\widehat{A}$ is essentially free, then $A$ separates the ideals of $A\rtimes_r\Gamma$.

Let $\pi:E\to G$ be a continuous second countable saturated Fell bundle over a non-compact groupoid $G$, and let $C_r^*(G,E)$ denote its reduced C-algebra. A completion of the asso…

Let $G$ be a groupoid with abelian stabilizer subgroups, and let $G^{(0)}/G$ denote its orbit space. The stabilizers are said to vary continuously when the corresponding map into t…