10 problems

Let $k,q\in\mathbb{N}$, $v\in\mathbb{C}$, and $\omega,\lambda\in\mathbb{R}_{>0}^2$. Let $H^{q,k}(z,v,\omega,\lambda)$ be the integral defined by … where $J$ and $\mathfrak{g}$ are…

Let $\mathcal{Z}_{\alpha}(\boldsymbol{\theta})$ and $\mathcal{Z}_{\alpha}^{\eta}(\boldsymbol{\theta})$ denote the zero-spin and spin-$\eta$ pure partition functions, respectively,…

Let ${}_{p}\Psi_q$ denote the Fox–Wright function, and consider the series in equations,, and, each expanded about the relevant point in the variable $1-z$. Radius-of-convergence c…

Asymptotic balance conjecture. As $\epsilon\to0$,

Let $\mathcal{F}$ be a singular holomorphic foliation in $\mathbb{C}\mathbb{P}^2$. Let $L_1$ and $L_2$ be two non-invariant projective lines, and let…

Let $W^{\vee}_0=W^{\vee}$ be the Gepner point and $W^{\vee}_{\infty}=\prod_i x_i$ the large complex structure point in the deformation space of $W^{\vee}$. Let the corresponding Sa…

Let $\alpha$ be an entire function. On a nonsingular analytic surface, let $u$ solve the Cauchy problem for … with entire data. Let $q$ solve … and let $v$ solve the corresponding…

Three-dimensional Neumann-oval conjecture. $W$ can be analytically continued throughout $\Omega\setminus B$. This is a proposed higher-dimensional analogue of the Schwarz potential…

Let $\Gamma$ be a nonsingular analytic surface, and consider the Cauchy problem for Laplace's equation on $\Gamma$ with real-entire data. Let $u$ be its solution, and let $w$ be th…

Let $G=\mathrm{SL}(n,\mathbb R)$, let $\mathrm{Fl}(\mathbb R^n)$ and $\mathrm{Fl}(\mathbb C^n)$ denote the real and complex complete flag varieties, and let…