9 problems

Generic-singularity conjecture. By numerical experiments, the generic singularities on surfaces of constant positive Gaussian curvature should be cuspidal edges and swallowtails.

Let $m,n$ be positive integers, and let $G(m,m+n;\mathbb{C})$ denote the complex Grassmannian. A holomorphic 2-sphere is linearly full when it is not contained in a proper totally…

Let $m,n$ be positive integers, and let $G(m,m+n;\mathbb{C})$ denote the complex Grassmannian. A holomorphic 2-sphere is linearly full when it is not contained in a proper totally…

Let $m,n$ be positive integers, and let $G(m,m+n;\mathbb{C})$ denote the complex Grassmannian. A holomorphic 2-sphere in this Grassmannian has degree $\mathrm{d}$ and constant curv…

Let $m,n$ be positive integers, and let $G(m,m+n;\mathbb{C})$ denote the complex Grassmannian. A holomorphic 2-sphere in this Grassmannian has degree $\mathrm{d}$, defined as its a…

Let $G(2,n)$ be the complex Grassmann manifold of 2-planes in $\mathbb{C}^n$, and let $\mathcal{K}_{2,n}^{fh}$ denote the set of constant curvatures of linearly full holomorphic tw…

Strichartz's conjecture. The function $A(t)$ is bounded and decays on the order of $O(t^{-1/4})$ as $t\to\infty$ in the flat or negative-curvature case. This is numerical evidence…

Let $G(m,n)$ be the complex Grassmannian, represented by an $n\times m$ matrix field, and let $r$ be the positive integer defined by … so that the associated constant Gaussian curv…

Let $(x_{\mathbf{i}},\nu_{\mathbf{i}})$ and $(y_{\mathbf{i}},\mu_{\mathbf{i}})$ be independent principal contact elements obtained as trajectory surfaces of a discrete rotating mot…