7 problems

Let $f:X\to S$ be a smooth projective morphism of smooth complex varieties, and fix $s\in S$. Let $\Theta_{X/S}$ be the quantity on the Dolbeault moduli space appearing in the sour…

Consider elliptic cluster algebras associated with elliptic generalizations of cluster mutations, and elliptic isomonodromic deformation flows. Elliptic-mutation conjecture. Ellipt…

Let $q$-isomonodromic systems have monodromy manifolds, and let elliptic dilogarithms be the generating functions associated with the proposed transformations. Elliptic cluster str…

Its–Prokhorov rational primitive conjecture. There exists a function $G(P_a,Q_a,t_k)$, rational in the variables $\{P_a\}$, $\{Q_a\}$ and $\{t_k\}$, such that

Its–Prokhorov symplectic-form conjecture. There exists a constant $\gamma\in\operatorname{\mathbb{C}}$ such that

Let $M$ be the moduli space of pairs $(C,Q_0)$, let $\mathcal O=\mathcal O(g,m)$ be the space of data $(C,Q_0,Q_1,Q_2)$ described above, and let $X^\#$ be the space equipped with t…

An isomonodromy system is a differential system whose monodromy data remain constant under deformation, and a singularity reduction is a gauge transformation that regularizes the s…