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Explore the mathematical foundations of infinite circle packings through this 48-minute conference talk that examines both geometric structures and dynamical processes in these complex mathematical objects. Delve into the intricate relationships between geometry and dynamics as they apply to infinite arrangements of circles, investigating how these packings behave and evolve over time. Learn about the theoretical frameworks used to analyze infinite circle packings, including their structural properties and the mathematical tools needed to understand their behavior. Discover the connections between circle packing theory and broader areas of mathematics, including dynamical systems and geometric analysis. Gain insights into current research directions and open problems in this specialized field of mathematics, presented as part of the Fields-CNAM Nonlinear Days 2025 conference focusing on dynamical, geometric, and random structures and processes.
