The Smale conjecture for RP^3 and minimal surfaces

In the early 80s Hatcher proved the Smale Conjecture, asserting that the diffeomorphism group of the three-sphere retracts onto its isometry group.  The corresponding problem for RP^3 was open nearly 40 years, and resolved only in 2019 by a detailed study of Ricci flow with surgeries.  I will explain a new proof using minimal surfaces.  This is joint work with Yevgeny Liokumovich.