4 problems

Let $f$ and $g$ be the polynomial system in two variables … where $a,b,r,s,t$ are positive reals. Itenberg–Roy conjecture. Such a system has at most $2$ real solutions. Li and Wang…

Fewnomial root-count conjecture. The maximum number of non-degenerate roots of $F$ in the positive orthant is

Kouchnirenko's conjecture. The bound $s_1\cdots s_n$ is sharp for the number of positive solutions of $C\cdot x^A=0$ when $C$ has real coefficients.

Consider the system … where the coefficients are nonzero real numbers and the exponent vectors are distinct nonzero real vectors. The polynomial upper bound conjecture. The correct…