9 problems

Let $\mathcal{C}$ be a smooth and compact $A_\infty$-category. Its noncommutative Hodge–de Rham spectral sequence is the spectral sequence associated with the cyclic-homology filtr…

Let $X \subset \mathbb{P}^5$ be a smooth cubic fourfold, and let its K3 Hodge atom be the Kuznetsov component $\mathcal{A}_X$ of $D^b\operatorname{Coh}(X)$. Interpreting the semior…

Let $X\to Y$ be a contraction of a smooth projective variety. Let $\operatorname{K}^{\mathrm{top}}(X)_\mathbb Q$ denote rational topological $K$-theory, equipped with its canonical…

Let $(M,\Omega_I)$ be holomorphic symplectic, set $\omega_u=\operatorname{Re}(u^{-1}\Omega_I)$ and $B_u=\operatorname{Im}(u^{-1}\Omega_I)$, and let $F(M,\omega_u,B_u)$ be the corre…

Let $(M,\Omega_I)$ be a holomorphic symplectic manifold, and let $RW(M,\Omega_I)$ denote its Rozansky–Witten 2-category. Rozansky–Witten Hochschild and cyclic homology conjecture.…

Let $C$ be a smooth proper dg-category. Categorical non-commutative Hodge structure conjecture. There is an entirely categorical way to produce a non-commutative Hodge structure fr…

Let $\mathbf{C}$ be a dg-category. Under suitable conditions, suppose there is a semi-infinite enhancement consisting of a commutative differential graded algebra…

Let $p$ be a $\mathbb{C}((q))$-point of $\hat{\mathcal{M}}_{cpx}(X^\circ)$ such that $X^\circ_p$ is smooth. Write $HP_\bullet(\mathsf{DCoh}(X^\circ_p))$ for the periodic cyclic hom…

Let $\EuC$ be a proper and smooth $A_\infty$ category. Its negative cyclic complex $CC^-_\bullet(\EuC)$ carries the Hodge filtration, which induces a spectral sequence. We say that…