10 problems

Let $\mathcal{X}$ be an orbifold with coarse moduli space $X$, and let $\phi\colon Z\to X$ be a crepant resolution. Iritani's conjecture. There exists an isomorphism … induced by a…

Let $G=\operatorname{GL}_r$. Let $\mathcal{B}\subset(\mathrm{B}_{\operatorname{GL}_r}^{\mathrm{red}})^{\mathrm{cl}}$ be an open subset, and set … Let…

Let $C:\operatorname{Spec} R\to \mathcal{M}_{cub}$ be a cubic curve, and let $\widehat{C}$ denote its formal completion, a formal group over $R$. Write…

Let $C$ be a smooth projective curve of genus $g$, let $L$ be a line bundle on $C$ with $l=\deg L>2g-2$, and let $B^L$ be the Hitchin base. For rank $r$, numerical invariant $hi$,…

Period-preserving involution conjecture. The space $F_{1,1}$ admits a period-preserving birational involution $S\leftrightarrow S'$ such that

Let $\pi_M:(M,\sigma)\to B$ be an integrable system, with partial Fourier–Mukai transform $\phi_{\mathrm{FM}}$, sheaf of Kähler differentials $\Omega_M^k$, and decomposition-theore…

Let $G$ be a complex reductive group, let $X$ be a smooth complex projective curve, let $G^{\vee}$ be its Langlands dual group, and let $T^*Bun_G(X)$ and $T^*Bun_{G^{\vee}}(X)$ be…

Let $\mathscr{L}^{\mathcal{X}}\subset\mathscr{V}^{\mathcal{X}}$ and $\mathscr{L}^{\mathcal{Y}}\subset\mathscr{V}^{\mathcal{Y}}$ be the equivariant genus-zero Gromov–Witten Lagrangi…

Let $\mathcal A$ be the Hitchin base, let $H:M\to\mathcal A$ be the Hitchin fibration, and let $\overline P$ be the universal Poincaré sheaf from the global conjecture. For each…

Let $C$ be the underlying smooth projective curve, let $r$ and $d$ be the rank and degree, let $M=\mathcal M(d,r,\omega_C)$ be the moduli space of $S$-equivalence classes of Higgs…