7 problems

For each $d$, let $P_d(y)$ be the Poincaré polynomial of the corresponding moduli space, let $\widetilde P_{d,\chi}(y)$ be the Poincaré series of the stack of semistable sheaves, a…

Sharpness conjecture. In the notations of Theorem …

The iterated balanced filtration is a canonical sequential filtration associated to a point of a noetherian algebraic stack with affine diagonal that admits a good moduli space and…

Let $X$ be a Calabi-Yau manifold with Kähler metric. Let $L$ be an almost calibrated exact Lagrangian brane in $D^bFuk(X)$ with a Harder-Narasimhan decomposition … whose distinguis…

Let $\mathcal{J}(r)$ be the Frobenius instability locus in the coarse moduli space of semistable vector bundles of rank $r$ and degree $0$. For a vector bundle, its Harder–Narasimh…

Let $C$ be a Teichmüller curve of genus $g$. Let $boldsymbol{ u}=( u1, u2, u3, u4)=(1,w2,ldots,wg)$ denote the normalized Harder–Narasimhan data of the Hodge bundle, and let…

Let $(P,d\sigma)$ be the moment polytope of a polarised toric variety with canonical boundary measure $d\sigma$. A pair $(Q,d\sigma)$ is semistable when $\mathcal{L}_A(f)\geq 0$ fo…