4 problems

Fatou's conjecture. Functions in $\mathcal{S}$ admit no invariant line fields supported on their Julia sets.

Quasiregular NILF conjecture. Every such map $f$ has no invariant conformal structure that is non-trivial on its Julia set.

Let $f$ be a polynomial, an entire transcendental function with finitely many singular values, or a rational map that is not double covered by an integral torus endomorphism. An in…

Let $f:\widehat{\mathbb{C}}\to\widehat{\mathbb{C}}$ be a rational function, and consider measurable invariant line fields supported on its Julia set. Flexible Lattès maps conjectur…