9 problems

A unimodular rigid geometric structure is a rigid geometric structure preserved together with a volume form; examples include a pseudo-Riemannian metric or an affine connection tog…

Let $G$ be a Lie group acting in the setting of a Fukaya category $\mathcal{F}uk(M)$. Teleman's topological Lie group action conjecture. The group $G$ should act topologically on…

Let $G$ be a compact Lie group acting on a manifold $M$, and let $G\ltimes M$ be the associated action groupoid. Write $\mathcal{A}_{G\ltimes M}$ for its convolution algebra and…

Classification conjecture. Pseudo-Riemannian manifolds with an essential conformal group should be classifiable.

Let $W$ be an arbitrary closed manifold on which $SU(2)$ acts smoothly and non-trivially. Let $s\colon BSU(2) \to B\operatorname{Diff}(W)$ be the induced map on classifying spaces,…

Let $G$ be an abelian Lie group of dimension $k$. A codimension-one faithful Anosov action is an Anosov action of $G$ whose unstable direction has dimension one and which is faithf…

Translation-groupoid representation conjecture. Every orbifold groupoid can be represented by a translation groupoid with locally free group action.

Quotient-orbifold conjecture. Every orbifold is equivalent to a quotient orbifold arising from a smooth, almost free Lie group action on a smooth manifold.

Local-freeness conjecture. The action is everywhere locally free.