2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/160512We give a summary on spectral techniques for finite dimensional algebras and study its link to singularity theory. In particular, we offer a contribution to the categorification of the Milnor lattice of two-dimensional singularities through triangulated categories naturally associated with a weighted projective line.42 pages to appear in "Trends in Representations of Algebras and Related Topics" (Editor: Andzej Skowronski)Representation TheoryAlgebraic Geometry16G20; 16G50; 14G60text