9 problems

Let $W$ be a Liouville filling of contact dimension $2n-1$, let $SH^*_+(W)$ denote its positive symplectic cohomology, let $SH^*_{+,S^1}(W)$ denote its positive $S^1$-equivariant s…

The terminal-singularity conjecture. If the singularity $\mathbb{C}^n/G$ is terminal, then

Let $[i]$ be a closed geodesic whose corresponding SFT generator in $\mathbb{R}\times M$ is $q_i$. Consider a building configuration that may contribute to the differential of…

Let $Y$ be the unit cotangent bundle of a hyperbolic surface, and let $(M=\Sigma \times Y,\xi_k)$ be the corresponding $5$-dimensional contact manifold from Corollary … have untwis…

Let $[i]$ be a closed geodesic and let $q_i$ be the corresponding SFT generator in $\mathbb{R}\times M$. A building configuration is a holomorphic-curve building that may contribut…

For each $n\geq 1$ and $k\geq 1$, consider the corresponding example of Theorem 5d, formed using a suitable $(2n-1)$-dimensional manifold $Y$, and denote the resulting contact mani…

Let $Y$ be the unit cotangent bundle of a hyperbolic surface, and let $(M=\Sigma\times Y,\xi_k)$ be the corresponding $5$-dimensional contact manifold of Theorem 5d. These examples…

Algebraic torsion conjecture. Then $(V,\xi)$ has algebraic $1$-torsion, and it is also algebraically overtwisted if $N$ contains any blown down boundary components.

For integers $k\geq 1$ and $n\geq 2$, let $(M,\xi)$ denote a closed $(2n-1)$-dimensional contact manifold, and let algebraic torsion and stable symplectic fillings be understood in…