12 problems

For each $t\in\mathbb{R}$, $X\in\mathfrak{g}$, let $\Theta(M,t)(X):=\int_M e^{-itd_X\lambda^{M_{\mathcal O}}}\alpha(X)$, and let $\Theta_0^{\mathcal O}$ denote the generalized-func…

Let $X$ be a Hamiltonian $T$-manifold with moment map $mu$, and let $X//_tT=mu^{-1}(t)/T$ be the smooth symplectic reduction. Let $Pi_X^{\rm eq}$ denote the equivariant quantum vol…

Let $X$ be a monotone almost complex manifold with a Hamiltonian action of a group $G$, moment map $\mu$, and symplectic quotient $X/\!/G=\mu^{-1}(0)/G$. Let $\mathcal{F}(X)$ denot…

Let $X$ be a Liouville manifold equipped with a Hamiltonian $S^1$ action such that the fixed locus $X^{S^1}$ has codimension four and there are no finite non-trivial stabiliser gro…

Generic symmetry-reduced integrability conjecture. A generic $G$-invariant Hamiltonian system on $P^N_M$ is integrable only when these geometric conditions are such that symplectic…

Let $(M,Z,\omega,\mu)$ be a compact connected Hamiltonian $G$-space, where $G$ is compact and connected, $M$ is prequantizable, and $Q_G(M,Z,\omega)\in R(G)$ is its equivariant qua…

Let $G$ be a reductive group with maximal compact subgroup $K$. Let $H<G$ be a $\theta$-stable Cartan subgroup, and let … be a cuspidal parabolic subgroup corresponding to $H$, wit…

Let $\bar{X}_W$ be the symplectic reduction in the geometric phase, let $H_{\rm CR}^*(\bar{X}_W;\Lambda)$ denote its Chen–Ruan cohomology, and let…

Let $G$ and $H$ be Lie groups and let $X$ and $Y$ be smooth manifolds on which $G$ and $H$, respectively, act properly. Assume that the orbit spaces $X/G$ and $Y/H$ are diffeomorph…

Hyperkähler Kirwan surjectivity conjecture. The hyperkähler Kirwan map is surjective.

Let $(M,\omega,\mu)$ satisfy (H), be convex at infinity, and be semipositive. Let $\varphi$ be a map … satisfying the equivariant Novikov condition, and let $\varphi_*$ be the indu…

Let $(X,\omega_X,G,\mathbf J)$ be a Hamiltonian $G$-space for $G$ a reductive group, and let $\mathcal X_{red}$ be the derived Marsden–Weinstein quotient associated with a coadjoin…