Hodge Theory

Hodge Theory is a branch of mathematics that studies the relationship between algebraic geometry and differential geometry. Specifically, it explores how the shape of a geometric object can influence the types of functions defined on it, particularly harmonic functions. By analyzing these functions, Hodge Theory reveals insights about the underlying structure of the object, such as its holes and dimensional features. This theory has applications in various fields, including physics, complex analysis, and topological data analysis, helping to understand complex shapes and their properties through a deeper mathematical framework.