Foundations of Hastings-Levitov Models and Loewner Evolution

Exploring the intersection of complex analysis and stochastic growth processes can seem daunting without a clear conceptual foundation. This course provides a structured introduction to conformal mapping techniques, Loewner differential equations, and Hastings-Levitov aggregation models. You will gain a thorough grounding in the mathematical machinery used to analyze planar growth phenomena, capacity-driven processes, and boundary behaviors. What you'll learn: - Understand the core terminology and geometric principles of conformal mappings in the complex plane - Master the formulation of Loewner differential equations driven by continuous functions - Analyze discrete aggregation frameworks including Hastings-Levitov strike and bump dynamics - Apply mathematical techniques to estimate cluster diameters and scaling limits - Study the foundational steps behind key results such as the Carleson-Makarov estimates for regularized processes - Explore modern computational and analytical perspectives on random planar growth models Starting with fundamental definitions of analytic functions and slit mappings, the text systematically progresses into continuous Loewner evolutions and theoretical growth analysis. This course is designed for learners, researchers, and students seeking an accessible, step-by-step introduction to geometric function theory without assuming prior advanced background in random conformal geometry. Begin reading today to strengthen your mathematical foundation in modern planar growth theory.