7 problems

Projective-space conjecture. We conjecture that

Segal's stability conjecture. The stability theorem for spaces of rational curves should extend to the spaces of maps from ${\bf CP}^{m}$ to ${\bf CP}^{n}$ for $m>1$.

Let $n\geq 2$, and consider the space of harmonic maps $S^2\longrightarrow\mathbb{CP}^n$ with fixed energy and fixed degree. Connectedness conjecture. This space is connected. The…

Rotation-invariant classification conjecture. The only projectively induced and rotation-invariant Kähler–Einstein manifolds are open subsets of

Let $\mu:\mathbb{N}\to\{0,1\}$ be defined by … Let $X$ be a finite-dimensional CW-complex homotopy equivalent to $\prod_{i=1}^k S^{m_i}\times\mathbb{C}P^{n_i}$, with each $m_i>0$,…

Let $k$ be a positive integer, and let $\operatorname{Conf}^n\mathbb{C}P^k$ denote the configuration space of $n$ ordered distinct points in complex projective $k$-space. Write…

Observable diameter limit conjecture. One has