7 problems

Let $(M,g)$ be a Riemannian manifold and let ${\mathcal{F}}$ be a singular Riemannian foliation on $M$. Consider the partition $\overline{{\mathcal{F}}}$ of $M$ by the closures of…

Let $\mathcal{F}$ be a regular foliation of rank $p$ on a smooth projective variety $X$, and let $L$ be an ample line bundle on $X$. Foliated Fujita conjectures. The line bundle ……

Let $(M,\mathcal F)$ be a codimension-one foliation of a closed manifold that is transversely $C^2$, with exceptional minimal set $\Lambda$. A semi-exceptional leaf is a boundary l…

Let $(M,\mathcal F)$ be a codimension-one foliation of a closed manifold that is transversely $C^2$, with exceptional minimal set $\Lambda$. Dippolito's conjecture. There exists a…

Let $L$ be a proper leaf of a codimension one $C^2$ foliation on a compact manifold. The end-type invariant $\xi(L)$ is the invariant used to classify the ends of $L$. Cantor finit…

Let $f$ be a partially hyperbolic diffeomorphism with an invariant center foliation whose leaves are all compact. A foliation is uniformly compact when all its leaves are compact a…

Applications conjecture. The theory developed in this paper should have applications to foliation theory and to the integration problem of sh-Lie algebras.