7 problems

Let $\mathcal{R}$ be a plane-curve-singularity ring with branches indexed by $1\le i\le\kappa$, and let $\sigma=(c_1\ge\cdots\ge c_\kappa>0)$. Define the motivic superpolynomial ……

The (a,t)-deformed $F_K$ conjecture. There should exist a four-variable function satisfying

Rectangular DAHA-superpolynomial positivity conjecture. The coefficients of $H\!D_{r,s}(j\omega_i;q,t,a)$ are positive integers. After the displayed transformation, the resulting p…

Let $Y_{m/n}$ be the set of $m/n$ Dyck paths, let $v(D)$ be the set of internal vertices of $D$, and let $\beta(P)$ be the stated vertex statistic. Let…

Let $\mathcal{P}_{n,m}^{\lambda}(u,q,t)$ be the stabilized superpolynomial and define its reduced version by … Cherednik's duality conjecture. For the transposed partition…

Let $\mathcal{P}_{n,m}^{\lambda,N}(q,t)$ be the DAHA superpolynomial associated with a partition $\lambda$ in rank $N$. Cherednik's stabilization conjecture. There exists a polynom…

Let $m$ and $n$ be coprime positive integers, let $\mathcal{P}_{n,m}(u,q,t)$ denote the superpolynomial, and let $D$ range over lattice paths below the main diagonal in an…