Number Theory Through Geometry, Dynamics and Illustration - Lecture 2

Explore advanced topics in number theory with dynamical and geometric aspects in this 54-minute lecture by Katherine Stange at the Centre International de Rencontres Mathématiques. Delve into continued fractions, Diophantine approximation, and Apollonian circle packings, focusing on both theoretical and experimental tools. Experience the role of visualization and illustration in mathematical research as the lecture emphasizes visual and dynamical approaches to background material, including continued fractions, quadratic forms, hyperbolic geometry, Minkowski space, and Kleinian groups. Discover current research areas such as the geometry of Diophantine approximation and continued fractions in the complex plane, algebraic starscapes, Schmidt arrangements, and the surprising relationships between Apollonian circle packings and preceding topics. Recorded during the thematic meeting "Renormalization and Visualization for packing, Billiard and Surfaces" on July 11, 2023, this lecture is part of CIRM's Audiovisual Mathematics Library, offering features like chapter markers, keywords, enriched content, and multi-criteria search capabilities.