The symplectic Thom conjecture

The minimal genus problem is a fundamental question in smooth 4-manifold topology. Every 2-dimensional homology class can be represented by a surface. But how small can this surface be? A generation ago, techniques from gauge theory were used to solve this in a large class of 4-manifolds with extra geometric structure, namely symplectic 4-manifolds. Recent work on trisections if 4-manifolds has revealed an deep connection with symplectic geometry and gives a new perspective on this result.