Zoom-Meeting: https://wwu.zoom.us/j/97461739978 Abstract: It is widely expected that a simply connected closed 4-dimensional Riemannian manifold M with positive sectional curvature must be homeomorphic to the 4-sphere or the complex projective plane. Using a new take on classical techniques, we prove this to be the case if M is d-pinched with d = 1/(1+3 sqrt 3) ~ 0.161, that is, if all sectional curvatures of M lie in the interval [d,1]. We also give new bounds on the Euler characteristic and signature of simply connected d-pinched 4-manifolds for any value of d > 0. The main tools used are convex algebro-geometric and optimization insights on sets of d-pinched curvature operators. This is based on joint work with M. Kummer and R. Mendes.