7 problems

Let $B$ be the inside of a generic ellipse, let $\rho\to0$ with $\rho t\to\infty$, and define … For an ellipse $x_1^2+\alpha^2x_2^2=1$ with $\alpha$ Diophantine, let…

Let $B$ be the region being dilated, let $t$ be the inner radius, and let $\rho=\rho(t)$ be the annulus width. The microscopic regime is characterized by $\rho t$ being constant, a…

Let the width of a family of elliptical annuli tend to zero while the area of the annuli tends to infinity, and let the number of lattice points in the annulus be normalized to hav…

Let $E_\tau$ be the elliptic curve with parameter $\tau\in\mathbb{H}$, and let $\Sigma=\{p_1,\ldots,p_n\}\subseteq E_\tau$, where $n$ is even. Let $AP_\Sigma(\tau)$ be the associat…

Let $\tau\in\mathbb{H}$, let $\Sigma=E_\tau[2]$, and let $(\alpha_1,\ldots,\alpha_4)\in(2\mathbb{Z})^4$. The apparent space $AP_\Sigma(\tau)$ parametrizes the relevant apparent dat…

Let $\mathcal{H}^{e\text{RS}}_k$ be the elliptic Ruijsenaars-Schneider Hamiltonians for $k=1,\dots,N-1$, and let $\mathcal{Z}^{\text{RS}}(\textbf{a},\textbf{x})$ be a function of t…

Let $N-1$ degrees of freedom of the quantum double elliptic (DELL) system be described by the current $\mathcal{O}(z)$ and let $\mathcal{Z}^{DELL}_{\text{inst}}(p,x_1,\dots, x_N)$…