8 problems

Linear growth conjecture on the universal cover. The limit exists and satisfies

Let $G_\omega(M)$ be the symplectomorphism group equipped with the Hofer-like norm $\|\cdot\|_{HL}$. For a geodesic $\{\phi_t\}_{t\geq 0}$ in this metric with nonzero flux, write…

Let $L_0$ and $L_1$ be Lagrangian isotopic submanifolds, and let $K:L_1\rightsquigarrow L_0$ be a Lagrangian cobordism. Let $d(L_0,L_1)$ denote the minimal flux distance, defined b…

Let $(M,\omega)$ be a closed connected symplectic manifold. Write $SSympeo(M,\omega)$ for the group of strong symplectic homeomorphisms, and let $Sympeo_0(M,\omega)$ be the identit…

Let $(M,c11)$ be a closed connected symplectic manifold. Write $SSympeo(M,c11)$ for the group of strong symplectic homeomorphisms and $Hameo(M,c11)$ for its normal subgroup of Hami…

Let $\rho$ denote the density parameter in the stochastic parking model, and let the formal flux be the flux obtained in the unperturbed process while the typical flux is the limit…

Let $\rho$ be the particle density, let $h$ be the critical density, let $\phi_{\pi(n)}(\rho;n)$ be the finite-$n$ flux in the zero-range model with parameter $\pi(n)$, and let…

Let $\rho$ be the particle density, let $h$ be the critical density, let $\phi(\rho;n)$ be the finite-$n$ typical flux, and let $\phi^*$ be the maximal-equilibrium-state flux. Let…