Explore the fascinating intersection of probability theory and geometric measure theory in this 53-minute lecture by Alexander Volberg. Delve into Besicovitch's classical theorem on self-similar Cantor sets and its implications for the Buffon needle problem. Investigate the probability of a Buffon needle intersecting the δ-neighborhood of Cantor sets as δ approaches zero, uncovering unexpected connections to Fourier and Complex analysis, Combinatorics, Algebra, Diophantine equations, and Number theory. Examine the Gelfond-Baker theory stemming from Hilbert's 7th problem and its relevance to this intriguing mathematical question.