3 problems

Gizatullin's conjecture. If $f^*$ has infinite order on $Pic({\cal X})$, then ${\cal X}$ should have an anti-canonical curve.

Let $X$ be a compact complex surface and let $T:X\to X$ be an automorphism with positive topological entropy. Let $\mu$ be the unique measure of maximal entropy, and let $(X,T)$ be…

Let $S$ be a compact connected orientable surface and let $f\colon S\to S$ be an orientation-preserving homeomorphism. A virtual homological spectral radius for $f$ is the homologi…