10 problems

Let $\cA=C^\infty(\mathbb{T}^2)\rtimes\mathbb{R}$, with generators $u_1,u_2$ for the torus part and $v_t$ for the crossed-product action, and let $D$ be the Dirac-type operator def…

Let $\mathcal{A}_1=\mathcal{D}_{L^2}(\mathbb{R}^{2N})$ be the algebra of Moyal multipliers acting on the relevant Hilbert space, let $\mathcal{B}(\mathbb{R}^{2N})$ denote the propo…

Fix real numbers $C$, $a$, and $b$. Consider quantum Riemannian $1$-spaces with measure whose associated Hilbert space comes from a unital involutive algebra and a state, with non-…

Vanishing Einstein functional conjecture. The Einstein spectral functional vanishes.

Dolbeault–Dirac spectral triple conjecture. The point spectrum of $D_{\overline{\partial}}$ has finite multiplicity and tends to infinity. Consequently,

Let $\mathcal{O}_q(G/L_S)$ be an irreducible quantum flag manifold of weak Gelfand type, and let $(\Omega^{(bullet,bullet)},\kappa)$ be its covariant Kähler structure, unique up to r…

Let $\mathbb{C}_q[G/L_S]$ be an irreducible quantum flag manifold, and let $\Omega^{(0,\bullet)}$ be the subcomplex of its Heckenberger--Kolb calculus. Denote by…

Categorification conjecture. The category of finite even $S^o$-real spectral triples over $\mathbb{C}$ and spectral triple morphisms is equivalent to the category of finite-dimensi…

Continuum spectral-triple conjecture. The Kasparov module

Let $SG$ denote the Sierpiński gasket and let $(A,H,D)$ be a spectral triple for $C(SG)$ inducing the geodesic distance on the gasket. Suppose that it is summable for every…