Conformal geometry is a branch of mathematics that deals with geometric properties that are preserved under conformal mappings. Conformal mappings are transformations that preserve angles locally, but can change distances and shape. In conformal geometry, the focus is on studying geometric objects and structures that remain invariant under conformal transformations. This area of research has applications in various fields such as differential geometry, complex analysis, and mathematical physics. Key topics in conformal geometry include conformal manifolds, conformal field theory, and conformal mapping theory.