8 problems

Let $\mathrm{Gr}_p(\operatorname{\mathbb{C}}^{p+q})$ carry its symmetric metric, where $p\geq 3$ and $p+q$ is odd. An infinitesimal Einstein deformation is a first-order deformatio…

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 $k<n$, let $G(k,n)$ be the complex Grassmannian of $k$-planes in $\mathbb{C}^{k+n}$, and let … be its rational cohomology ring. If $h$ is a graded ring endomorphism with…

Let $n_1,\ldots,n_k$ be distinct positive integers, let $n=n_1+\cdots+n_k$, and for $\mathbb{F}\in\{\mathbb{R},\mathbb{C}\}$ define … where $U_{\mathbb{R}}(n)=O(n)$ and…

Vanishing conjecture. If $\phi$ vanishes on $H^2(G_{n,k};\mathbb{Z})$, then $\phi$ vanishes in every positive degree.