10 problems

Corner-factor conjecture. There is a canonical determinant $\operatorname{det}_{\angle}'\mathcal N_{\partial P}$ of the Neumann jump operator on a piecewise real-analytic curve wit…

Let a Jordan domain have finitely many corners with angle parameters $\alpha_j$, and let the truncated Grunsky determinant be regularized by subtracting its logarithmic divergence.…

Let $\alpha$, $p$, and $j\in\mathbb{Z}_{\ge 0}$ be as above, and let $\mathcal{Q}_{\pm,j}^{(\alpha)}(E;p)$ denote the eigenvalues of the graded operators $\hat{\mathbf{Q}}_\pm(E)$…

ZabrodinWiegmann determinant conjecture. For a quasi-harmonic potential,

Fix $d_0$ and $k>-2$, and let $r$ and the Gaudin and BLZ systems be as in the source. Define $Q_{+,r}(\lambda)=\lambda^rQ_+(\lambda)$ for the Gaudin spectral determinants, and use…

Fix $d\geq1$, $k>-2$, and $l>-\frac12$, and let $\bar k,\bar l$ be related to $k,l$ as in the source. Let the BLZ trivial-monodromy system and its spectral determinant…

Let $\mathcal{F}$ be the expression defined in Eq., and let $\log \det'\Delta_{\rm L}$ denote the logarithm of the regularized spectral determinant of the Laplacian. Consider their…

Functional-equation conjecture. The displayed identity is conjectured to hold for every coupling $k$. The relation is supported in the source by spectral computations and small-…

General matching-condition conjecture. The same formula should hold for a broader class of matching conditions than the two cases considered.

General-boundary-condition spectral-determinant conjecture. By continuity from the cases of continuous functions and continuous derivatives, the $\zeta$-regularised spectral determ…