Joint work with D. Bravo (UdelaR-Uruguay) and Octavio Mendoza (UNAM - Mexico).

The Igusa-Todorov functions are a generalisation of the projective and the injective dimensions, see [IT]. I will begin by defining them and by providing examples. Then I will explain a closely related tool, namely the Igusa-Todorov algebras introduced by Jiaqun Wei in [W].
A triangular finite dimensional algebra over a field is an algebra which Gabriel's quiver has no oriented cycles. I will present a characterisation of triangular algebras which are Igusa-Todorov. For this purpose, we have generalised some of the results obtained by Jiaqun Wei in [W2].

[IT] Igusa, Kiyoshi; Todorov, Gordana. On the finitistic global dimension conjecture for Artin algebras. Representations of algebras and related topics, 201-204, Fields Inst. Commun., 45, Amer. Math. Soc., Providence, RI, (2005).
[W] Wei, Jiaqun. Finitistic dimension and Igusa-Todorov algebras. Adv. Math. 222, no. 6, 2215--2226, (2009).
[W2] Wei, Jiaqun. Finitistic dimension conjecture and conditions on ideals. Forum Math. 23, no. 3, 549--564, (2011).