Explore classical and innovative applications of geometric valuation theory in the realms of geometric probabilities and integral geometry in this 38-minute lecture. Delve into Cauchy-Kubota and kinematic formulas for convex bodies, and discover recent findings on convex functions presented by Monika Ludwig, in collaboration with Andrea Colesanti and Fabian Mussnig. Gain insights into the intersection of geometry and probability theory through this advanced mathematical discourse from the Hausdorff Center for Mathematics.