toric geometry

Toric geometry is a branch of mathematics that studies shapes called "toric varieties," which are geometric objects built from simple combinatorial data like fans and polytopes. These shapes have a rich structure that connects algebra, geometry, and combinatorics, often allowing complex shapes to be understood and constructed from simpler, symmetrical parts. Think of it as a way to translate between algebraic equations and geometric shapes using combinatorial tools, making it easier to analyze and classify complex high-dimensional objects with symmetrical properties.