Arnold's seminar, 18th Nov 2003 M. Kazarian Simple matrix singularities (after Goryunov, Zakalyukin, Bruce, Tari) The talk is devoted to the study of singularities of two-parameter families of symmetric matrices. The theory provides a remarkable example of classical Singularity Theory that was so popular in 80th on the seminar and has nearly disappeared now. It relates in a wonderful way such objects as quasihomogeneous filtrations, normal forms, versal deformations, bifurcation diagrams and their K(\pi,1)-properties, vanishing homology, monodromy, Dynkin diagrams, ADE, and other things making the flavor of Singularity Theory.