5 problems

Kikyo–Pillay's conjecture. If $T_\sigma$ has a model companion, then $T$ has the definable multiplicity property.

A strongly minimal set is a definable set whose definable subsets are finite or cofinite; its algebraic closure induces a combinatorial geometry, which is non-locally modular when…

Zilber's conjecture. Every non-locally modular geometry of a strongly minimal set behaves like a field.

Positive-dimensional recursive model conjecture. If some positive-dimensional model $M\models T$ is recursive, then all models of $T$ are recursively presentable.

Recursive-spectrum trichotomy conjecture.