11 problems

Poisson convexity conjecture. The image

Let $\Gamma$ be a quasi-symplectic groupoid, let $X$ be a Hamiltonian $\Gamma$-space with momentum map $J$, and let ${\cal O}\subset P$ be an orbit of the groupoid. The reduced spa…

Let ${\mathcal T}_{3,0}$ be the Teichmuller space of flat $SL_2(\mathbb C)$-connections on a smooth Riemann surface of genus three. Consider the cluster algebra constructed in Sect…

Categoroid equivalence conjecture. There is an equivalence of categoroids between $\textbf{Poiss}^{Ext}$ and $\textbf{RRSGpd}$:

Equivalence conjecture. Any two regular relational symplectic groupoids integrating $M$ are equivalent.

Symplectic-groupoid quantization conjecture. The quantization of the symplectic groupoid produces the same $C^*$-algebra as the quantum-space construction for…

BS-groupoid conjecture. Since these Poisson manifolds are in general non-unimodular, the BS groupoids should arise from the multiplicative integrability of the modular function.

SU(3) reduction conjecture. The reduction of $L_1$ corresponds to the union of the zero section of $T^*(G/G)$, the conormal bundle $N^*(K/G)$, and a full cotangent fiber of $G/G$ a…

Equivalence conjecture. There is an equivalence of categroids

Connectedness conjecture. Theorem 1 holds also when the $s$-fibers are not connected.

Let $P$ be a strongly regular Poisson manifold whose simply connected symplectic leaves are the fibres of a smooth fibration $P\to M$. Assume that the lattice of differentials of p…