Density functions for filtrations of homogeneous ideals

A density function for an algebraic invariant is a measurable function on $\mathbb{R}$ that evaluates the invariant on a real scale. This approach encapsulates richer information about the invariant without requiring additional data. In this talk, we introduce and develop density functions $f_{I_n}$ corresponding to filtrations $\left\{I_n\right\}_{n \in \mathbb{N}}$ of graded ideals within a standard graded domain $A$. This is joint work with Suprajo Das and Sudeshna Roy.