16 problems

Let $\lambda$, $\mu$, $\lambda'$, and $\mu'$ be partitions in $\mathbb{Z}^n$. For vectors $x,y\in\mathbb{Z}^n$, define … A symmetric polynomial is Schur nonnegative if it is a nonn…

Casian–Kodama conjecture. The degree $\eta(w_*)$ of $p(q)$ is related to the multiplicity $d$ of the singularity of ${\mathcal D}_0$ at $p_o$. Namely, $d$ is given by the minimal d…

Casian–Kodama conjecture. The number of blow-ups is also given by the number of real roots of those Schur polynomials for a specific variable.

A Thom–Boardman class is a singularity class indexed by a sequence of nonnegative integers, and its Thom polynomial is the universal cohomology class representing the locus of maps…

Three-variable Schur maximal-rank conjecture. For all sufficiently large $d$, the following holds: if $\lambda\in F$, then $s_\lambda$ fails to be a maximal rank element on $A$; if…

Self-conjugate-grid uniform conjecture. For every $0\leqslant k\leqslant n-1$,

Schur-polynomial pointwise conjecture. For all $0\leq k<n\leq t$,

For a positive integer $m$, let $\widetilde X_{12}^{(a)},\widetilde X_{13}^{(a)},\widetilde X_{23}^{(a)}$ for $1\leq a\leq m$ be the formal variables associated with the multiple g…

SNP conjecture. For $t\in\mathbb Z_{>0}$, we have

Let $\lambda$ be a partition whose nonzero parts are distinct, and let $P_\lambda$ be its Schur $P$-function. Schur-$P$ conjecture. The normalized function … is Lorentzian for ever…

Let $\lambda,\mu\in\mathbb{Z}_{\geq0}^n$ be partitions satisfying $\lambda_i\geq\mu_i$ for every $i$, and let $s_{\lambda/\mu}$ be the skew Schur polynomial. Skew-Schur conjecture.…

Let $\lambda$ be a strict partition, meaning a decreasing sequence of positive integers, and let $P_\lambda(x_1,\ldots,x_m)$ be its Schur $P$-polynomial. Schur-$P$ conjecture. The…

Let $\lambda/\nu$ be a skew Young diagram, and let … be its skew Schur polynomial, where the sum is over semistandard Young tableaux of shape $\lambda/\nu$ with entries in $[m]$. S…

Strict unimodality conjecture. If the Durfee square size of $\lambda$ is large enough, then the coefficients of $s_\lambda(1,q,\ldots,q^{m})$ are strictly unimodal.

The Kostka-support conjecture. For sufficiently large $r$, the sequence

The multivariate root-circle conjecture. Under some mild non-degeneracy conditions on the partitions,