3 problems

Nondifferentiability conjecture. If $f$ is non-differentiable at infinitely many points, then $C$ is 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…