8 problems

Let $I^{(k,r)}_m$ be the ideals in the polynomial representation $V$ of the double affine Hecke algebra representation $mathcal{H}n^{(k,r)}$, with…

Superquadratic non-redundancy conjecture. For the concrete example $p=3$ and $f(x)=(x_1+x_2+x_3)(x_1+x_2+x_3-1)$, there exists $\delta>0$ such that

Let $k$ be a positive integer and define … A quadratic representation means a polynomial representation of this predicate of degree at most two. Khanna et al.'s conjecture. For all…

Let $f:\{0,1\}^n\to\{0,1\}$ be a Boolean function, represented by its unique multilinear polynomial $f(x)=\sum_s f_s\prod_{i\in s}x_i$. Define its sparsity by…

Suppose $c_0=j/k$ with $k$ and $j$ relatively prime positive integers, and $2\leq k\leq n$. Let $\mathbf{C}[\mathfrak{h}]$ be the polynomial representation, and let…

Let $Z_{p,m}$ and $Z_{p,m}'$ be the submodules defined above, and let $E_1$ be the first member of the corresponding filtration of submodules. EZ submodule conjecture. With the not…

Covering-number conjecture. The covering number of every such polynomial is $d^{o_M(1)}$. This would bound the complexity of the obstructions underlying the paper's constant-round…

Minimal polynomial-representation conjecture. Every $d$-dimensional polytope in ${\mathbb{R}}^d$ has a polynomial representation