Explore the Finsler--Thorpe trick for curvature operators in dimension 4 and its application in combination with twisted spinor methods to demonstrate area-extremality for scalar curvature in compact 4-manifolds. Delve into a 46-minute lecture that examines how these techniques prove local area-extremality in regions of positive sectional curvature on 4-manifolds. Learn about the joint work of Renato Bettiol from Lehman College, CUNY, and McFeely Jackson Goodman from UC Berkeley, as presented at the Institut des Hautes Etudes Scientifiques (IHES).