10 problems

Nondifferentiability conjecture. If $f$ is non-differentiable at infinitely many points, then $C$ is not semi-algebraic.

Non-algebraic perp conjecture. If $a_n,c_n>0$ are chosen as above, then

Schur-ideal perp conjecture. The perp of this Schur ideal is not a semi-algebraic subset of $\mathbb{R}^3$.

Non-semi-algebraic unit-ball conjecture. The unit ball determined by the constructed $3$-idempotent operator algebra is not a semi-algebraic set.

Non-semi-algebraic interpolation-body conjecture. For a sufficiently pathological uniform algebra, there will exist interpolation bodies that are not semi-algebraic.

Let $\alpha,\beta,\gamma,\delta,\varsigma\in\mathbb R$ satisfy … and let $\varrho_+(\alpha,\beta,\gamma,\delta)$ denote the unique positive root of the discriminant quadratic descr…

Let $\mathcal{P}$ and $\mathcal{Q}$ be finite sets of polynomials in $\mathbb{R}[X_1,\ldots,X_k]$, with the same notation and hypotheses as in Theorem B-B; in particular, let…

Polynomial independent-set conjecture. There is a constant $\epsilon=\epsilon(d,t,s)$ such that one can find an independent set $P'$ with

Let $\mathbf{K}\subseteq\mathbf{B}$ be semi-algebraic sets, and consider a hierarchy of volume estimates based on polynomial approximations using a polynomial basis. A basis has a…

Let $\mathbf{K}$ be a basic semi-algebraic set contained in a simple set $\mathbf{B}$, and consider polynomial approximation schemes for volume or integration on $\mathbf{K}$ using…