7 problems

Let $\mathcal{S}$ be an admissible spectral curve with $x,y$ satisfying … A quantisation of $P$ is an operator $\hat{P}(\hat{x},\hat{y};\hbar)$ of the form … where…

Let ${\mathcal W}$ be a point of the Sato Grassmannian with wave function $\Psi$ and quantum spectral curve operator ${\mathtt P}_{\mathcal W}$, so that … For a tau-function with a…

Exponential formula. The solution should have the WKB expansion

Consider the Weierstrass spectral curve … Let $\hat{P}(\hat{x},\hat{y};\hbar)$ be a quantum curve of the form … where the $A_i(x)$ and $B_j(x)$ are polynomials in $x$. A Weierstras…

Let $K\subset S^3$ be a knot with $A$-polynomial curve $A_K(m,\ell)=0$. Let $\hat A_K$ be the quantisation obtained from topological recursion: calculate the functions $S_k(u)$ by…

Let $K\subset S^3$ be a knot, and let $A_K(m,\ell)=0$ be its $A$-polynomial curve. Put $(m,\ell)=(e^u,e^v)$, and let $S_0(u)$ be defined by the wave-function equations in the sourc…

Let ${\cal S}$ be a spectral curve, let $\psi({\cal S},\hbar;p_1,p_2)$ be its formal Baker–Akhiezer kernel, and define $\Omega_p(q)=\frac{B(p,q)}{dx(p)}$ and…