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The classical degree-genus formula computes the genus of a nonsingular algebraic curve in the complex projective plane. The well-known Thom conjecture posits that this is a lower bound on theÌýgenus of smoothly embedded, oriented and connected surface in CP^2.ÌýÌý

The conjecture was first proved twenty-five years ago by Kronheimer and Mrowka, using Seiberg-Witten invariants.Ìý In this talk, we will describe a new proof of the conjecture that combines contact geometryÌýwith the novel theory of bridge trisections of knotted surfaces.ÌýÌý

Notably, the proof completely avoids any gauge theory or pseudoholomorphic curve techniques.