Alexander Volberg: The Probability of Buffon Needle to Land Near Cantor Set

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.

Intro
Randomness
Super good directions
Main theories
Proof
Estimate
Set of small values
Estimate from below
Property of set of small values
The proof
The real problem
Another definition
Theorems