Ricci Flow with Surgery

Ricci Flow with Surgery is a process used in mathematics to understand and simplify complex shapes, called manifolds. It involves gradually "smoothing out" irregularities in the shape's curvature over time, similar to heating and reshaping a rough object. When certain regions develop singularities or become extremely distorted, the process temporarily cuts out these problematic parts (surgery) and replaces them with more regular pieces. This iterative method helps mathematicians analyze the shape's fundamental structure and has been crucial in proving major results like the Poincaré Conjecture.