Self-Similar Sets and Measures on the Line

Explore the fascinating world of fractal geometry in this 49-minute lecture on self-similar sets and measures on the line. Delve into central objects of interest, including classical examples like the Cantor set, Sierpiński triangle, Koch snowflake curve, and Bernoulli convolutions. Examine the problem of determining the dimension of these objects, focusing on recent developments from the past four years. Learn about key concepts such as the Minkowski dimension, open set condition, dimension of measures, exponential separation condition, and algebraic parameters. Gain insights into proofs and mathematical techniques used in this field. Access accompanying slides for visual support and deeper understanding of the presented material.