8 problems

Let $M$ be a hyperbolic 3-manifold and let $\rho:G\to \operatorname{SL}(2,\mathbb C)$ be a lift of the discrete faithful representation associated to its hyperbolic structure. Supp…

Let $L_0$ be a single circle in the disc $mathbb{D}$ bounding a disc of area $Afrac{1}{2}$. For each integer $igeq 2$, embed the disc into a sphere of area $(i+1)A$ and let…

Reduction conjecture. The reduction of $\mu_X^{EP}$ to $\Sigma$ is also an Entov–Polterovich quasimorphism: there exists an Entov–Polterovich quasimorphism

Let $G$ be the group of autoequivalences of the category under consideration, and let the shifting numbers assign numerical invariants to elements of $G$. Fan–Filip's quasimorphism…

Homogenized signature conjecture. For every positive braid $\beta$,

Let $G$ be a finitely presented group, and let $g_n$ be obtained by a length-$n$ random walk, conditioned to lie in $[G,G]$. Suppose that, for every $\epsilon>0$, there is a positi…

Let $G$ be any finitely generated group, let $S$ be a finite symmetric generating set, and suppose that the space $Q(G)$ of homogeneous quasimorphisms modulo homomorphisms is finit…

Let $\Gamma$ be a group and let $\varphi\colon \Gamma\to\mathbb{R}$ be a homogeneous quasimorphism. Write $\partial\varphi$ for its coboundary, $[\partial\varphi]_{\mathrm{b}}$ for…