Geometric Invariant Theory

Geometric Invariant Theory (GIT) is a branch of mathematics that studies how geometric objects, like shapes or figures, behave under transformations such as rotation or scaling. It seeks to identify properties of these objects that remain unchanged, or invariant, despite these changes. GIT is particularly useful when analyzing systems that exhibit symmetry, allowing mathematicians to classify shapes and solve problems in geometry and algebra. It bridges fields like algebraic geometry and representation theory, making it a crucial tool in understanding the structure of mathematical objects and their relationships.