11 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 ……

Let $\scD^{(1)}_{\ell}$ be the $\ell$-dimensional module singled out among the four modules in the shortening regime, with basis indexed by $0\leq j\leq \ell-1$. Let…

Let $q$ and $t$ satisfy the shortening condition defining the $(k+1)$-dimensional module $\repV_{k+1}$ of the spherical double affine Hecke algebra, with basis indexed by…

Let $N$ be a positive integer, let $q_u=q^{\frac{1}{2}}$, and let $S_{N-1}(\mathcal{A}_{(1,2)})$ be the indicated Chebyshev-type expression in the DAHA operator…

Let $\boldsymbol{c}$ be a simple closed curve on the genus-two surface $\Sigma_{2,0}$, and let $\overline{P}_n(q_u,x_u,x_d;\boldsymbol{c})$ denote its reduced DAHA invariant. The pa…

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 $\mathcal{H}$ and $\mathcal{H}^{\checkmark}$ denote the two DAHA-type algebras considered in the paper, and let $\mathcal{B}_q$ be the associated braid-group representation. Co…

Let $K=K_{r,s}$ be a knot with $r,s\in\mathbf{Z}$, and let $b$ be a dominant weight for all $B_m$ with $m\ge n\ge2$. Type-B hyper-polynomial conjecture. There exists a polynomial…

Let $H\!D_{r,s}(b;q,t,a)$ have positive coefficients, let $\mathcal{H}=\bigoplus\mathcal{H}_{i,j,k}$ be the triply graded space for the torus knot $\{r,s\}$ and weight $b$, and let…

Let $b\in P_+$ correspond to a Young diagram $\mu_b$ with rows of lengths $m_i$, and let $b_i=m_i\omega_1$. Write $\operatorname{ord}$ for the order of $\mu_b$. Evaluation conjectu…

Let $K=K_{r,s}$ be a torus knot with $r,s\in\mathbf{Z}$, let $R$ be a root system, and let $b\in P_+$ be a dominant weight. Define … Here $P_b$ is the symmetric Macdonald polynomia…