20 problems

Bloch's conjecture. For every $\gamma\in A^2(Y\times X)$, the induced action $Gr^*_F\gamma$ depends only on $cl(\gamma)$.

Core decomposition equality. The core decomposition of $K$ satisfies

Let $g\geq 1$, let $\mathcal{D}_g$ be the Dehn quandle of a closed orientable surface of genus $g$, and let $\mathbb{Z}[\mathcal{D}_g]$ be its integral quandle algebra. An element…

González-Alonso–Torelli conjecture. Such a deformation can have rank

Let $S$ be a geodesic surface of genus $g$, and let $c(S)$ denote its cop number. Mohar's surface conjecture. … The paper describes this as a tough conjecture because it implies th…

Canonical-degree bound conjecture. There exist constants $A$ and $B$, depending only on $X$, such that for every integral curve $C$ on $X$,

Super-maximization conjecture. One has

Let $\Sigma_{g,n}$ be a surface of genus $g$ with $n$ punctures, let $\mathcal{C}(\Sigma_{g,n})$ be its curve algebra, let $\mathcal{C}(\Sigma_{g,n})'$ be the subalgebra generated…

Let $\Sigma_{g,n}$ be a punctured surface, let $\mathcal{C}(\Sigma_{g,n})_{\mathbb{C}}$ be its complexified curve algebra, and let $\mathcal{T}^{d}(\Sigma_{g,n})$ be its decorated…

Let $\Sigma_{g,n}$ be a surface of genus $g$ with $n$ punctures, and let $\mathcal{A}(\Sigma_{g,n})$ and $\mathcal{U}(\Sigma_{g,n})$ denote its cluster and upper cluster algebras,…

Let $\Sigma_{g,n}$ be a surface of genus $g$ with $n$ punctures, and let $\mathcal{A}(\Sigma_{g,n})$ denote its cluster algebra. Non-finite generation conjecture. For $g\geq 2$,…

Let $\alpha$ and $\beta$ be orthogeodesics. They are length equivalent when they have equal lengths. A reflection involution is an involution reflection acting on the relevant hyperb…

Kikuta–Takahashi's conjecture. One has

Let $S$ be a smooth projective complex surface with $K_S\not\equiv 0$ that admits no minimal elliptic fibration. Let $Z$ be the union of all $(-2)$-curves, and let…

Let $X$ be a Barlow surface, and let $\mathrm{D}(X)$ denote its derived category. Barlow surface phantom conjecture. The category $\mathrm{D}(X)$ has an exceptional collection of l…

Let $S$ be a surface with geometric genus $p_g(S)=1$ and irregularity $q(S)=2$. Let $A^1_{hom}(S)_{\mathbb{Q}}$ be the group of homologically trivial divisor classes with rational…

Signed Talaska formula. There exists a map

Let $X$ be a quasi-projective surface of log-general type, defined over a number field $K$, and let $\mathcal O_S$ be the ring of $S$-integers for a finite set of places of $K$ con…

Let $S$ be a surface, let $(G,p)$ be a framework generic on $S$, and let $(\omega,\lambda)$ be an equilibrium stress for $(G,p)$. Write $\Omega_S(\omega,\lambda)$ for its stress ma…

Reduced-regulator vanishing conjecture. The map $\underline{r}_{3,1}$ is zero.