7 problems

Symplectic singularities conjecture. For all $(V,G)$, the modified complex symplectic quotient has symplectic singularities and is graded Gorenstein.

The paper studies equivariant and nonabelian symplectic quotients in integral $K$-theory, where the results avoid torsion difficulties that obstruct analogous statements in integra…

Let $T$ be a torus and let $\leq i\leq \dim T$. For each subtorus $\tau\subset T$, let $\mathcal{A}_\tau$ denote the corresponding summand of the module $\mathcal{A}$, and set … Le…

Let $A$ be a faithful weight matrix in standard form, and let $\gamma_0(A)$ denote the first Laurent coefficient of the Hilbert series associated with the corresponding symplectic…

In certain admissible cases, including the relevant $\mathbb{S}^1$-cases, let $\Phi^{-1}(0)$ be a cone on a manifold $L$, and let $T$ be the torus acting on $L$. Non-rational-homol…

Let $V$ be a symplectic vector space and let $G<\mathsf{Sp}(V)$ be finite, assuming that $V/G$ admits a symplectic resolution. Poisson and Hochschild homology conjecture. The canon…

Let $X$ be a Fano manifold and let $g(t)$ be a normalized Kähler-Ricci flow. Set $\tau=e^t-1$, and let $\bar g$ be the corresponding $S^1$-invariant metric on $X\times\mathbb C$ sa…