2 problems

Let $D\geq 1$, let $F\in\mathbb C[x_1,\ldots,x_D]$ be irreducible of degree $d$, and assume each partial derivative $F_{x_1},\ldots,F_{x_D}$ is not identically zero. The higher-dim…

Let $F\in\mathbb C[x,y,z]$ be an irreducible polynomial, and let $A,B,C\subset\mathbb C$ have size $n$. The Elekes–Szabó incidence conjecture. In the balanced case, the bound for g…