A survey on Igusa-Todorov functions.

This article is a survey of Igusa-Todorov functions, which were introduced by Igusa and Todorov in their study of the finitistic dimension conjecture. These homological functions map objects in the category of right finitely generated modules over an Artin algebra to the natural numbers, generalizing the notion of projective dimension. Using these functions, Igusa and Todorov demonstrated that the finitistic dimension of Artin algebras with representation dimension at most three is finite. In recent years, several studies have focused on these functions and their associated dimensions. Notably, they have been employed as a key tool in proving the finitistic dimension conjecture for certain families of algebras. This article provides an overview of some of these recent developments