17 problems

Let $q$-conformal blocks be the blocks associated with the $q$-difference isomonodromic deformation problem for $q$-Painlevé VI, and let their Fourier transforms define tau functio…

The spectrum singularity average $A_N(t;)$ is related to the isomonodromy theory of the sixth Painlevé system. Jimbo's extension conjecture. The expansions of Jimbo given in Theore…

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…

Let $\tau(t)$ be one of the paper's $q$-isomonodromic tau functions, let $\hat{\tau}_{AB}$ denote a $q$-generalization of an Arinkin–Borodin tau function, and let…

Consider isomonodromic systems obtained by deautonomization of Goncharov–Kenyon dimer integrable models, and let topological string partition functions denote the corresponding par…

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…

Let a spectral curve be quantized by topological recursion, producing a Lax system, and let its associated non-perturbative partition function be defined. Non-perturbative partitio…

Let $K$ be a finitely generated field of characteristic zero, let $C$ be a curve over $K$, and let $(\mathscr{E},\nabla)$ be a vector bundle with connection on $C$. Choose an embed…

Let $\tau_{\mathrm{V}}(x)$ be the tau-function associated with the PV Schlesinger-type equation, defined through its logarithmic derivative by the expansion given above. An infinit…

Cecotti–Vafa conjecture. If

Convexity and asymptotic behavior conjecture. (a) The components of $\psi_{mat}(M_{3FN,\mathbb R}^{sing})\cap\mathbb R_{>0}\times V^{mat,a\cup c,\mathbb R}$ and of…

Consider the special solution of $P_{\mathrm{I}}^2$ studied in the paper and the corresponding solution of $P_{\mathrm{I}}^{(2,1)}$. A merging pole is a collision of poles of the s…

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…