7 problems

Let $M$ be a compact connected spin manifold, let $D_g$ be the Dirac operator for a Riemannian metric $g$, and call $g$ $D$-minimal when the kernel of $D_g$ is no larger than force…

Let $M$ be a compact spin manifold of dimension at least three, and let $h_g$ denote the dimension of the space of harmonic spinors for a Riemannian metric $g$ on $M$. Harmonic-spi…

Let $M^{2}\subset\mathbb{S}^{3}(1)$ be an embedded closed surface of genus one, and suppose that the curvature endomorphism satisfies $\Re|_{\slashed{E}}=0$. Let $\bar{\Gamma}_{1}$…

Lott's conjecture. The optimal constant is $C=4\pi$.

zGKN spectral convergence conjecture. The discrete spectrum of the Dirac Hamiltonian on zGKN should converge to the Bohr–Sommerfeld spectrum of the usual Hydrogen problem on Minkow…

Critical-coupling conjecture. Following Esteban, Lewin and Séré, one conjectures that

Boldt–Lauret–Schüth conjecture. If the two spin lens spaces are Dirac isospectral, then they are isometric. The claim is supported by computational evidence for spin lens spaces, w…