Explore quaternionic contact (qc) versions of the Almost Schur Lemma in this 45-minute lecture by Aleksander Petkov from Sofia University. Delve into estimations of the qc scalar curvature on compact qc manifolds, examining how it approaches a constant in relation to the norm of the [-1]-component and the trace-free part of the [3]-component of the horizontal qc Ricci tensor and torsion endomorphism. Investigate the necessary positivity conditions for these estimations and gain insights from Petkov's collaborative work with Stefan Ivanov on this advanced topic in quaternionic contact geometry.