ИСТИНА

Given a pair of real or complex algebraic varieties, it is of interest to obtain a local classification of real- or complex-analytic maps between them up to right equivalence (or up to certain other equivalence relations). When working on such a classification one usually imposes certain restrictions on the ``complexity’’ of the maps considered in terms of codimension, modality, etc.Moreover, when the source and target of the maps are endowed with actions of a group, it is natural to consider equivariant maps, i.e., maps that ``commute’’ with those group actions. Certain well-known classification results for singular multivariate functions, including those in the equivariant context, belong to V.I. Arnold, D. Siersma, and V.V. Goryunov. In my talk I will mention some more recent results and open questions related to the topic, as well as possible connections with the study ofparameter-dependent matrices, vector fields, and differential equations.