9 problems

Let $\omega$ be the permutation governing the switching algorithm, and let $\mathcal{O}\in\operatorname{Orb}(\omega)$ be one of its orbits. A genomic tableau is a tableau counted b…

Let $p:\mathfrak{Q}\to S$ be a quadric fibration of relative dimension $n+1$ over a smooth base, with fibers $\mathfrak{Q}_s$ of rank at least $4$, where $n$ is odd. Let…

Let $\langle Q_1,Q_2\rangle$ be a pencil of quadrics in $\mathbb{P}^{n+2}$ whose base locus is smooth in an odd-dimensional projective space. Let $C$ be the hyperelliptic curve ass…

Realizability conjecture for orthopositroids. Every orthopositroid $\mathscr{M}$ of type $(k,n)$ is realizable: there exists $X\in\operatorname{OGr}_{+}(k,n)$ such that…

Let ${\mathsf{OGr}}(k,V)$ be an orthogonal Grassmannian, and let the collections in the source be the semiorthogonal collections constructed in Theorems,, and. The orthogonal Grass…

Let $(\boxtimes,T)\in \operatorname{LR}(\alpha,\scalebox{.5}{\yng(1)},\beta,\gamma)$, where $\operatorname{LR}(\alpha,\scalebox{.5}{\yng(1)},\beta,\gamma)$ is the set of type B Lit…

Let $S$ range over the Schubert curves in the orthogonal Grassmannian $\operatorname{OG}$ constructed in the paper, and let $g_a(S)$ denote the arithmetic genus of $S$. Unbounded-g…

The Shapiro conjecture for $OG(n)$. If $s_1,\dotsc,s_m$ are distinct real numbers, then

Let $\varphi$ be a nondegenerate quadratic form on a vector space over a field $F$, and for a positive integer $d$ let $X_d$ be the variety of $d$-dimensional totally isotropic sub…