Donaldson's tamed-to-compatible conjecture
What the paper claims, in its own words
Proves Donaldson's tamed-to-compatible conjecture: every smooth almost complex structure on a closed four-manifold that is tamed by a symplectic form admits a compatible symplectic form. The almost complex structure stays fixed; the form's cohomology class may change.
The plain-language explainer for this entry is still coming.