8 problems

Let $F$ be a nonarchimedean local field, let $G$ be the group of $F$-rational points of a connected reductive algebraic group, and let $\mathcal H(G)_\Omega$ and…

Let $\mathcal{M}^{\mathrm{vert}}(\mathbb{P})$ be the vertical moduli space of a good degeneration, equipped with the global $(-1)$-shifted potential function $\mathbb{W}=f\cdot g$.…

Let $X$ be a smooth variety, let $V$ be a finite-dimensional complex vector space, and let $\bm{Z}$ be the derived zero locus associated with the function $f$ as in the constructio…

Stringy Euler-characteristic conjecture. The stringy Euler characteristic of $X$ can be computed as the Euler characteristic of an NCCR, computed via periodic cyclic homology.

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 $G$ be a discrete group. For an element $x$ in $G$, let $G_x$ denote its centralizer, let $N_x=G_x/\langle x\rangle$ be the reduced centralizer, and let…

Kontsevich–Pantev–Katzarkov conjecture. If $X$ is a "good enough" noncommutative space, then $HP_{\bullet}(X)$ carries a noncommutative Hodge structure. Equivalently,…

Let ${\mathcal G}$ be a reductive $p$-adic group and let ${\mathfrak s}$ be a point in the Bernstein spectrum of ${\mathcal G}$. Let…