Conformal Geometry and Dynamics

Conformal Geometry studies shapes and spaces where angles are preserved even if sizes change, like stretching or shrinking. It focuses on properties unaffected by such transformations. Dynamics, in this context, examines how these shapes evolve or behave over time under various rules or flows. Combining the two, conformal dynamics explores how structures that preserve angles change and move, revealing patterns and symmetries that help us understand complex systems—from geometric shapes to physical processes—by analyzing their invariant properties and long-term behavior.