Ricci flow is a mathematical process that deforms the shape of a Riemannian manifold, which is a space that has a notion of distance and angles. Introduced by Richard S. Hamilton in the 1980s, it smooths out irregularities in the manifold's geometry over time, similar to how heat diffuses through a material. The flow is governed by a partial differential equation that adjusts the metric of the manifold based on its curvature. This technique has significant implications in geometric analysis and has been instrumental in proving the Poincaré conjecture, a major problem in topology solved by Grigori Perelman.