1) The document discusses high-dimensional convex bodies and properties of random vectors uniformly distributed within such bodies. It focuses on understanding the distribution of projections of random vectors onto lines within the bodies. 2) A key open problem is the hyperplane conjecture, which proposes there exists a lower bound on the volume of any hyperplane section of a convex body. 3) Examples are given showing that for some simple bodies like cubes and balls, the distribution of projections resembles a Gaussian distribution, demonstrating "Gaussian-like behaviour".