4 problems

Let $M$ be a stably causal Lorentzian manifold whose sectional curvatures are much less than $1$, and let $\gamma$ be a timelike curve from $s$ to $t$ in $M$ whose radius of curvat…

Let $X_\Gamma$ be a derived $\Gamma$-space, let $\mathcal D_{\mathrm{coh}}(X_\Gamma)$ be its coherent derived category, and let $\mathsf{Phys}_\Gamma$ be the category of $\Gamma$-p…

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

Positive definiteness conjecture. For $q\in\mathbb{R}\setminus\{-1,0\}$, the pair $(\Omega^{(\bullet,\bullet)},\kappa)$ is a positive definite covariant Kähler structure.