From Simple Rules to Wild Universes: The Common Geometry of Chaos

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Infosys Prize Lecture

From Simple Rules to Wild Universes: The Common Geometry of Chaos

03:15 PM

September 17, 2026

Platinum Jubilee Auditorium (PJA), Indian Statistical Institute, Bangalore Centre

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From Simple Rules to Wild Universes: The Common Geometry of Chaos

Event

What connects planetary motion, weather unpredictability, and the geo metric beauty of fractals? The answer lies in dynamical systems–the study of how systems evolve over time under physical or mathematical rules. In this talk, we embark on a visual journey through complex dynamics and chaos. We explore how simple operations–from finding polynomial roots via Newton’s method to reflecting across geometric boundaries–give rise to rich fractal landscapes like the Mandelbrot and Julia sets. Finally, we will highlight how modern mathematics bridges the gap between two seemingly distinct mathematical worlds: repeated applications of algebraic functions and iterated reflections in circular mirrors. By fusing these different rules into a common “hybrid” dynamical system, we unlock new insights into real algebraic geometry, statistical physics, and universal fractal sets.

Speaker

Sabyasachi Mukherjee

Associate Professor, School of Mathematics, Tata Institute of Fundamental Research, Mumbai