Explore a comprehensive survey of volume inequalities in Euclidean space presented by Jeffrey VAALER from UT-Austin in this 59-minute BASIC NOTIONS SEMINAR talk. Delve into various problems and results concerning the volume of interesting subsets, focusing on identities and inequalities for convex sets and star-bodies. Examine a known theorem about the volume of cube intersections with subspaces, and learn about M. Gromov's conjectured generalization of this inequality. Gain insights into this accessible mathematical topic suitable for a general audience, covering fundamental concepts and advanced theories in volume geometry.