Toric Geometry
Toric geometry is the study of algebraic geometry and combinatorics focusing on the properties of toric varieties, which are algebraic varieties that can be constructed from certain combinatorial data. It investigates the relationships between the geometric properties of these varieties and the combinatorial structures associated with them, such as polytopes and fans. Toric geometry provides a powerful framework for studying complex algebraic varieties and has applications in areas such as mirror symmetry, symplectic geometry, and string theory.