14 problems

Zero-entropy conjecture. One has

Let $M\subset P_n(\mathbb{C})$ be a smooth hypersurface, where $n\geq 2$. Global minimality conjecture. Every such $M$ is globally minimal. This conjecture would remove the global…

Let $m=2t$. The reduced real $J$-theory group of complex projective space is generated by … Here $y_m=r\xi_m({\mathbb C})-2$, where $\xi_m({\mathbb C})$ is the complex Hopf line bu…

Let $\mathbb{CP}^{n}$ denote complex projective space. A complex structure on this underlying smooth manifold is an integrable almost-complex structure compatible with the relevant…

Let $M^{\prime}_{k,l}$ be the total space of the corresponding $S^3$-bundle over $\mathbb{C}P^2$, with Euler-class parameter $l$. It is known that … when $l$ is even. Escher's conj…

A Hamiltonian diffeomorphism of $\mathbb{C}P^n$ is a pseudo-rotation when it has the pseudo-rotation property described in the paper. The pseudo-rotation periodic-point conjecture.…

Let $H_0:\mathbb{T}\times\mathbb{C}\mathbb{P}^n\to\mathbb{R}$ be a time-dependent one-periodic Hamiltonian, where $\mathbb{C}\mathbb{P}^n$ carries the Fubini--Study symplectic form…

Let $V_d$ be a nonsingular algebraic hypersurface of degree $d$ in $\mathbb{CP}^{n+1}$. Here, “simplest” means having minimal topological complexity among representatives of the ho…

Let $(X,g,J)$ be a Kähler manifold with positive Ricci curvature, and consider the volume among Kähler metrics satisfying the relevant positive Ricci-curvature normalization. Folkl…

Let $F:H^{2n+1}(\ker \delta)\to H^{2n+1}(\ker \delta)$ be the map of Ricci iterations up to diffeomorphism near the rescaled Fubini–Study metric $g$ on $\mathbb{CP}^n$ satisfying…

Let $\mathbb{C}P^n$ carry the Fubini–Study symplectic form $\omega_{\operatorname{FS}}$. A Lagrangian torus $L\subset \mathbb{C}P^n$ is extremal when it realizes the relevant Lagra…

Let $L$ be a Lagrangian torus in $\mathbb{C}\mathbb{P}^n$. Call $L$ extremal if $A_{\rm min}(L)=c_L(\mathbb{C}\mathbb{P}^n)$, and call it monotone if its Maslov class is positively…

Let $(\mathbb{CP}^2,g_{FS})$ be the Fubini–Study metric. If the ordered TT-spectrum of $(-\Delta_L)$ is $0<\mu_1=32<\mu_2<\mu_3<\cdots$, define … At each value $\tau_i$, consider t…

Let $G$ be a compact (semi)simple subgroup of $\SU{N}$ for some $N$, and let $\mathcal O$ be a Lagrangian orbit of $G$ in $\CP^{N-1}$. Hamiltonian stability conjecture. If $G$ admi…